Mathematical logic Books

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Book SynopsisIn fact, perhaps the most significant sources of new activity have been the applied areas of Linguistics and Computer Science (including Artificial Intelligence), where many intriguing new ideas have appeared presenting further challenges to temporal logic.Trade ReviewFrom reviews of the first edition: `Overall this is an admirable work. I believe it will change and enrich the field.' Steven Kuhn, Journal of Symbolic Logic, 52 (3) (1987) `...the book...will be most useful to anyone, newcomer or expert, with an interest in the logic of time.' John Burgess, Journal of Philosophical Logic, 13 (3) (1984) Table of ContentsI / Temporal Ontology.- I.1. / Primitive Notions.- I.2. / Points.- I.3. / Periods.- I.4. / Points and Periods.- I.5. / Events.- II / Temporal Discourse.- II.1. / Choice of Languages.- II.2. / Instant Tense Logic.- II.3. / Extended Tense Logic.- II.4. / Point Talk and Period Talk.- Appendix A / On Space.- Notes.- List of Important Principles.- Index of Names.- Index of Subjects.- Appendix “Sept Ans Après”.- Additional References.

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Book SynopsisHowever, the problem is to understand what knowledge means, to find ways of representing knowledge, and to specify automated machineries that can extract useful information from stored knowledge. One may say that knowledge is summarized and organized data - at least the kind of knowledge that computers can store.Table of ContentsI. Theoretical Foundations.- 1. Knowledge.- 1.1. Introduction.- 1.2. Knowledge and Classification.- 1.3. Knowledge Base.- 1.4. Equivalence, Generalization and Specialization of Knowledge.- Summary.- Exercises.- References.- 2. Imprecise Categories, Approximations and Rough Sets.- 2.1. Introduction.- 2.2. Rough Sets.- 2.3. Approximations of Set.- 2.4. Properties of Approximations.- 2.5. Approximations and Membership Relation.- 2.6. Numerical Characterization of Imprecision.- 2.7. Topological Characterization of Imprecision.- 2.8. Approximation of Classifications.- 2.9. Rough Equality of Sets.- 2.10. Rough Inclusion of Sets.- Summary.- Exercises.- References.- 3. Reduction of Knowledge.- 3.1. Introduction.- 3.2. Reduct and Core of Knowledge.- 3.3. Relative Reduct and Relative Core of Knowledge.- 3.4. Reduction of Categories.- 3.5. Relative Reduct and Core of Categories.- Summary.- Exercises.- References.- 4. Dependencies in Knowledge Base.- 4.1. Introduction.- 4.2. Dependency of Knowledge.- 4.3. Partial Dependency of Knowledge.- Summary.- Exercises.- References.- 5. Knowledge Representation.- 5.1. Introduction.- 5.2. Examples.- 5.3. Formal Definition.- 5.4. Significance of Attributes.- 5.5. Discernibility Matrix.- Summary.- Exercises.- References.- 6. Decision Tables.- 6.1. Introduction.- 6.2. Formal Definition and Some Properties.- 6.3. Simplification of Decision Tables.- Summary.- Exercises.- References.- 7. Reasoning about Knowledge.- 7.1. Introduction.- 7.2. Language of Decision Logic.- 7.3. Semantics of Decision Logic Language.- 7.4. Deduction in Decision Logic.- 7.5. Normal Forms.- 7.6. Decision Rules and Decision Algorithms.- 7.7. Truth and Indiscernibility.- 7.8. Dependency of Attributes.- 7.9. Reduction of Consistent Algorithms.- 7.10. Reduction of Inconsistent Algorithms.- 7.11. Reduction of Decision Rules.- 7.12. Minimization of Decision Algorithms.- Summary.- Exercises.- References.- II. Applications.- 8. Decision Making.- 8.1. Introduction.- 8.2. Optician’s Decisions Table.- 8.3. Simplification of Decision Table.- 8.4. Decision Algorithm.- 8.5. The Case of Incomplete Information.- Summary.- Exercises.- References.- 9. Data Analysis.- 9.1. Introduction.- 9.2. Decision Table as Protocol of Observations.- 9.3. Derivation of Control Algorithms from Observation.- 9.4. Another Approach.- 9.5. The Case of Inconsistent Data.- Summary.- Exercises.- References.- 10. Dissimilarity Analysis.- 10.1. Introduction.- 10.2. The Middle East Situation.- 10.3. Beauty Contest.- 10.4. Pattern Recognition.- 10.5. Buying a Car.- Summary.- Exercises.- References.- 11. Switching Circuits.- 11.1. Introduction.- 11.2. Minimization of Partially Defined Switching Functions.- 11.3. Multiple-Output Switching Functions.- Summary.- Exercises.- References.- 12. Machine Learning.- 12.1. Introduction.- 12.2. Learning From Examples.- 12.3. The Case of an Imperfect Teacher.- 12.4. Inductive Learning.- Summary.- Exercises.- References.

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Book SynopsisThis book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. Beginning with the tenth Seminar, the intimate setting was retained, but each Seminar narrowed in theme;Table of ContentsI: Topos-like and Model-Theoretic Approaches.- 1: Classification of Extremal Subobjects of Algebras over SM-SET.- 2: M-valued Sets and Sheaves over Integral Commutative CL-Monoids.- 3: The Logic of Unbalanced Subobjects in a Category with Two Closed Structures.- II: Categorical Methods in Topology.- 4: Fuzzy Filter Functors and Convergence.- 5: Convenient Topological Constructs.- 6: A Topological Universe Extension of FTS.- 7: Categorical Frameworks for Stone Representation Theories.- III: Applications and Related Topics in Logic and Topology.- 8: Pointless Metric Spaces and Fuzzy Spaces.- 9: Fuzzy Unit Interval and Fuzzy Paths.- 10: Lattice Morphisms, Sobriety, and Urysohn Lemmas.- 11: The Topological Modification of the L-Fuzzy Unit Interval.- 12: A Categorical Approach to Fuzzy Relational Database Theory.- 13: Fuzzy Points and Membership.- Appendices.- Index of Categories.- Addenda et Corrigenda.

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Book SynopsisMorals of Thought and Speech Reminiscences.- What Has Logic Given to Philosophy?.- Classical, Relativistic and Constructivist Ways of Asserting Theorems.- Semantic Niches Or a Logic for Historians.- Objects and Properties.- Inferential Many-Valuedness.- A Ja?kowski-Style System of Computer-Assisted Reasoning.- Hilbert's Program: Incompleteness Theorems Vs. Partial Realizations.- The Logic of Objects.- Non-Fregean Semantics for Sentences.- Relational Semantics for Non-Classical Logics: Formulas are Relations.- Non-Standard Possible Worlds, Generalised Quantifiers and Modal Logic.- Against Straightforward Anti-Realism.- A Minimal Implicational Logic.- Knowledge Representation Systems for Groups of Agents.- Characterizing Propositional Logics by Formulas.- The Reification of Situations.- Intuitionism and Indeterminism (Tense-Logical Considerations).- Asymmetrical Relations.- Types of Predication.- Remarks on Extensionality and Intensionality.- On the Synthetic a priori.- Realism Vs RelatTable of ContentsPreface. Morals of Thought and Speech; J.M. Bochenski. What has Logic given to Philosophy? J.m. Bochenski. Classical, Relativistic and Constructivist Ways of Asserting Theorems; A. Grzegorczyk. Semantic Niches or a Logic for Historians; H. Hiz. Objects and Properties; J.J. Jadacki. Inferential Many-Valuedness; G. Malinowski. A Jaskowski-style System of Computer-Assisted Deduction; W. Marciszewski. Hilbert's Program: Incompleteness Theorems vs. Partial Realization; R. Murawski. The Logic of Objects; E. Nieznanski. Non-Fregean Semantics for Sentences; M. Omyla. Relational Semantics for Non-Classical Logics: Formulas are Relations; E. Orlowska. Non-Standard Possible Worlds, Generalized Quantifiers and Modal Logic; J. Pasniczek. Against the Straightforward Anti-Realism; T. Placek. A Minimal Implicational Logic; W.A. Pogorzelski. A Logic of Knowledge; C. Rauszer. Characterizing Propositional Logics by Formulas; T. Skura. The Reification of Situations; R. Suszko. Intuitionism and Determinism (Tense-Logical Considerations); K. Trzesicki. Asymmetrical Relations; P. Turnau. Types of Predication; E. Wojciechowski. Remarks on Extensionality and Intensionality; J. Wolenski. On the Synthetic a priori; B. Wolniewicz. Realism vs. Relativism in Philosophy of Science (Some Comments on Tarski's Theory of Truth; R. Wójcicki. Name Index.

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Book SynopsisThis volume contains a selection of papers presented at a Seminar on Intensional Logic held at the University of Amsterdam during the period September 1990-May 1991.Table of ContentsPreface. Beyond Accessibility: Functional Models for Modal Logic; J. van Benthem. Modal Logic and Attribute Value Structures; P. Blackburn. Interpreting Modal Natural Deduction in Type Theory; T. Borghuis. Modal Translations in K and D; K. Dosen. Logical Omniscience and Inconsistent Belief; J.O.M. Jaspars. Cautious Backtracking in Truth Maintenance Systems; C. Jonker. How Completeness and Correspondence Theory got Married; M. Kracht. Dyadic Modalities and Lambek Calculus; D. Roorda. A Logic with Progressive Tenses; V. Shehtman. The Complexity of Propositional Tense Logics; E. Spaan. On Total Awareness Logics; E. Thijsse. Completeness via Completeness: Since and Until; Y. Venema. The Feasibility of Defeat in Defeasible Reasoning; G. Vreeswijk. Index.

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Book SynopsisSince their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy.Table of ContentsPart 0: General Introduction; P. Ehrlich. Part I: The Cantor--Dedekind Philosophy and its Early Reception. On the Infinite and Infinitesimal in Mathematical Analysis, Presidential Address to the London Mathematical Society, November 13, 1902, E.W. Hobson. Part II: Alternative Theories of Real Numbers. A Constructive Look at the Real Number Line; D.S. Bridges. The Surreals and Reals; J.H. Conway. Part III: Extensions and Generalizations of the Ordered Field of Reals: the Late 19th-Century Geometrical Motivation. Veronese's Non-Archimedean Linear Continuum; G. Fisher. Review of Hilbert's Foundations of Geometry; Henri Poincaré (1902); Translated for the American Mathematical Society by E.V. Huntington (1903). On Non-Archimedean Geometry, Invited Address to the 4th International Congress of Mathematicians, Rome, April 1908, Giuseppe Veronese; Translated by Mathieu Marion (with editorial notes by Philip Ehrlich). Part IV: Extensions and Generalizations of the Reals: Some 20th-Century Developments. Calculation, Order, and Continuity; H. Sinaceur. The Hyperreal Line; H.J. Keisler. All Numbers Great and Small; P. Ehrlich. Rational and Real Ordinal Numbers; D. Klaua.

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Book SynopsisAt the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science.Table of ContentsIntroduction. Part I: Husserl and Frege: a Contribution to Elucidating the Origins of Phenomenological Philosophy; D. Føllesdal. Part II: The Criticism of Husserl's Argument against Psychologism in German Philosophy 1901--1920; M. Kusch. The Philosophy of Arithmetic: Frege and Husserl; R. Tieszen. Husserl and Frege on Substitutivity; C.O. Hill. Husserl's `Logic of Truth'; J.N. Mohanty. Part III: Husserl's Theory of Meaning and Reference; B. Smith. Reference, Experience, and Intentionality; D. Bell. Intentionality, Intuition and the Computational Theory of Mind; L. Haaparanta. The Integrity of the Mental Act: Husserlian Reflections on a Fregian Problem; D. Willard. Index of Names. Index of Subjects.

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Book SynopsisThe present collection of papers derives from a philosophy conference organised in the Sicilian town of M ussomeli in September 1991.Table of ContentsPreface. Abbreviations. Part 1: Philosophy of Language. The Social Aspect of Language; D. Davidson. Singular Terms; B. Hale. Philosophical Theorizing and Particularism: Michael Dummett on Wittgenstein's Later Philosophy of Language; D. Pears. Convention and Assertion; E. Picardi. Meaning Theory and Anti-Realism; D. Prawitz. Part 2: Philosophy of Mathematics. Anti-Realism and the Philosophy of Mathematics; G. Oliveri. Dummett and Wittgenstein's Philosophy of Mathematics; C. Penco. Vestiges of Realism; G. Sundholm. About `the Philosophical Significance of Gödel's Theorem': Some Issues; C. Wright. Part 3: Philosophy of Mind, Time and Religion. Dummett, Realism and Other Minds; A. Bilgrami. Truth, Time and Deity; B.F. McGuinness. Leaving the Past Where it Belongs; J. Schulte. Part 4: Dummett's Replies. Reply to Davidson. Reply to Hale. Reply to Pears. Reply to Picardi. Reply to Prawitz. Reply to Oliveri. Reply to Penco. Reply to Sundholm. Reply to Wright. Reply to Bilgrami. Reply to McGuinness. Reply to Schulte. Bibliography. Index.

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Book SynopsisA partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way.Table of ContentsPreface. Symbol Index. 1. Lattices. 2. Lattice-ordered groups. 3. Convex l-subgroups. 4. Ordered permutation groups. 5. Right-ordered groups. 6. Totally ordedered groups. 7. Embeddings of lattice-ordered groups. 8. Lattice properties in lattice-ordered groups. 9. Varieties of lattice-ordered groups. 10. Free l-groups. 11. The semigroup of l-varieties. 12. The lattice of l-varieties. 13. Ordered permutation groups and l-varieties. 14. Quasivarieties of lattice-ordered groups. Bibliography. Index.

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Book SynopsisBut we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions.Trade Review`It provides the foundations of uncertainty calculus that enables one to complement conventional system theory. ... I can highly recommend the book to those interested in the new developments in this interesting area and who are not afraid of some mathematics.' International Journal of Electrical Engineering Education, 33:3 (1996)Table of ContentsPreface. 1. Introduction. 2. Modeling Uncertainty. 3. Capacities and the Choquet Functional. 4. Information Measures. 5. Calculus of Fuzzy Concepts. 6. Fuzzy Measures and Integrals. 7. Decision Making. 8. Subjective Multicriteria Evaluation. 9. Pattern Recognition and Computer Vision. 10. Identification and Interpretation of Fuzzy Measures. Bibliography. Index.

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Book SynopsisQuantifiers: Logics, Models and Computation is the first concentrated effort to give a systematic presentation of the main research results on the subject, since the modern concept was formulated in the late '50s and early '60s.Table of ContentsPreface. Quantifiers, Some Problems and Ideas; M. Krynicki, M. Mostowski. Prologue; P. Lindström. On the Model Theory of Some Generalized Quantifiers; H.D. Ebbinghaus. Finite Generation Problem and n-ary Quantifiers; L. Hella, K. Luosto. Games and Trees in Infinitary Logic: a Survey; J. Väänäen. Theory of Linear Order in Extended Logics; H. Herre. Henkin Quantifiers; M. Krynicki, M. Mostowski. Continuous Operations on Spaces of Structures; X. Caicedo. Model Theory of Topological Structures; J. Flum. Computable Quantifiers and Logics over Finite Structures; J.A. Makowski, Y.B. Pnueli. Quantifiers in Natural Language. A Survey of Some Recent Work; D. Westerståhl. Index of Names.

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Book Synopsisto Volume II.- Quantifiers and Inference.- Operators on Branched Quantifiers.- Hilbert's ?-Symbol in the Presence of Generalized Quantifiers.- Partially Ordered Connectives and Finite Graphs.- Theories of Finitely Determinate Linear Orderings in Stationary Logic.- Definable Second-Order Quantifiers and Quasivarieties.- Quantifiers Determined by Classes of Binary Relations.- Decidability Results for Classes of Ordered Abelian Groups in Logics with Ramsey-Quantifiers.- On the Eliminability of the Quantifier There Exists Uncountably Many.- Quantifiers Definable by Second Order Means.- Generalized Quantifiers in Algebra.- On Ordering of the Family of Logics with Skolem-Löwenheim Property and Countable Compactness Property.- Pre-Ordered Quantifiers in Elementary Sentences of Natural Language.- Some Remarks on Zawadowsky's Theory of Preordered Quantifiers.- Index of Names.- Table of Contents to Volume I.Table of ContentsPreface. Quantifiers and Inference; J. van Benthem. Operators on Branched Quantifiers; M.A. Brown. Hilbert's Epsilon-Symbol in the Presence of Generalized Quantifiers; X. Caicedo. Partially Ordered Connectives and Finite Graphs; L. Hella, G. Sandu. Theories of Finitely Determined Linear Orderings in Stationary Logics; H. Herre. Definable Second-Order Quantifiers and Quasivarieties; A.A. Ivanov. Quantifiers Determined by Classes of Binary Relations; M. Krynicki. Decidability Results for Classes of Ordered Abelian Groups in Logics with Ramsey Quantifiers; W. Lenski. On the Eliminability of the Quantifier `There Exists Uncountably Many'; Z. Mijajlovic. Quantifiers Definable by Second Order Means; M. Mostowski. Generalized Quantifiers in Algebra; A.G. Pinus. On Ordering of the Family of Logics with Skolem-Löwenheim Property and Countable Compactness Property; M. Waclawek.DAGGER. Pre-Ordered Quantifiers in Elementary Sentences of Natural Language; M.W. Zawadowsky. Some Remarks on Zawadowski's `Theory of Preordered Quantifiers'; M.A. Brown. Index of Names.

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Book SynopsisDiscussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy.Table of ContentsPreface; J. Hintikka. Tracking Contradictions in Geometry: The Idea of a Model from Kant to Hilbert; J. Webb. Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematics; J. Hintikka. Kronecker on the Foundations of Mathematics; H.M. Edwards. The Mysteries of Richard Dedekind; D.C. McCarty. Frege's Letters; C. Ortiz Hill. Frege's Principle; R.G. Heck Jr. Husserl and Hilbert on Completeness; C. Ortiz Hill. Hahn's Über die nichtarchimedischen Größensysteme and the Development of the Modern Theory of Magnitudes and Numbers to Measure Them; P. Ehrlich. The Origins of Russell's Paradox: Russell, Couturat, and the Antinomy of Infinite Number; G. H. Moore. The Emergence of Descriptive Set Theory; A. Kanamori. Chance against Constructibility; J. von Plato. Thoralf Skolem, Hermann Weyl and `Das Gefühl der Welt als begrenztes Ganzes'; W. Boos. On Tarski's Background; J. Wolenski. Wittgenstein and Ramsey on Identity; M. Marion. On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle; J. Floyd. Gödel and Husserl; D. Føllesdal. Index of Names. Index of Subjects and Titles.

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Book SynopsisThis book is a study in the logic of questions (sometimes called erotetic logic). In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises.Table of ContentsIntroduction. 1. Erotetic Inferences and How Questions Arise. 2. Logical Theories of Questions. 3. Questions. 4. Semantics. 5. Evocation of Questions. 6. Generation of Questions. 7. Erotetic implication. 8. Erotetic Arguments. Bibliography. Index of Symbols. Index of Subjects. Index of Names.

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Book SynopsisNew Interpretations of Quantum Mechanics and the Theory of Knowledge.- Experiment, Entanglement and the Foundations of Quantum Mechanics.- Constructivism and Operationalism in the Foundations of Quantum Mechanics.- Computability in Quantum Mechanics.- Levels of Physical Theories.- A Constructivist Manifesto for the Physical Sciences Constructive Re-Interpretation of Physical Undecidability.- How Far Can We Formalize Language Games?.- What is a Random String?.- Strong Determinism vs. Computability.- Capturing Relativized Complexity Classes with Lindström Quantifiers.- Why Constructive Mathematics?.- Hypothetical Extensions of Constructive Mathematics.- Constructions as the Subject Matter of Mathematics.- Verificationism Then and Now.- Logic and Mathematics.- A Connection between Leibniz' Infinitely Small Quantities and the Analytical Hierarchy.- Extensional Equality in the Classical Theory of Types.- Hans Hahn and the Foundational Debate.- Crisis and Return of Intuition in Hans Hahn'sTable of ContentsBrief Editorial. Articles: The foundational debate. I. Physics. II. Complexity. III. Constructivism. IV. Hans Hahn. Report - Documentation. Reviews. Review Essay: Vienna-Berlin-Prague: Centenaries Carnap, Reichenbach, Zilsel; M. Stölzner. Activities of the Institute Vienna Circle. Index of names.

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Book SynopsisDoing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics.Table of Contents1. Introduction: Logic and the problem of meaning. 2. Roots of logical schematization. 3. Axiomatic systems. 4. Model theory. 5. Quantification. 6. Truth. 7. Denotation. 8. Meaning. 9. Criterial reconstruction. 10. Necessity. 11. Language and the world. References. Name index. Subject index.

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Book SynopsisInduction Using Term Orders.- New Uses of Linear Arithmetic in Automated Theorem Proving by Induction.- Productive Use of Failure in Inductive Proof.- Middle-Out Reasoning for Synthesis and Induction.- A Calculus for and Termination of Rippling.- Interaction with the BoyerMoore Theorem Prover: A Tutorial Study Using the ArithmeticGeometric Mean Theorem.Table of ContentsPreface. Induction Using Term Orders; F. Bronsard, et al. New Uses of Linear Arithmetic in Automated Theorem Proving by Induction; D. Kapur, M. Subramaniam. Productive Use of Failure in Inductive Proof; A. Ireland, A. Bundy. Middle-Out Reasoning for Synthesis and Induction; I. Kraan, et al. A Calculus for and Termination of Rippling; D.A. Basin, T. Walsh. Interaction with the Boyer-Moore Theorem Prover. A Tutorial Study Using the Arithmetic-Geometric Mean Theorem; M. Kaufmann, P. Pecchiari.

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Book SynopsisResolution Proof Systems: An Algebraic Theory presents a new algebraic framework for the design and analysis of resolution- based automated reasoning systems for a range of non-classical logics.Table of ContentsPreface. 1. Logical Preliminaries. 2. Propositional Resolution Proof Systems. 3. Propositional Resolution Logics. 4. Efficiency of the Deductive Process. 5. Theorem Proving Strategies. 6. Resolution Circuits. 7. First-Order Resolution Proof Systems. 8. Nonmonotonic Resolution Inference Systems. A. Resolution Counterpart of P2. B. Resolution Counterpart of P3. C. Resolution Counterpart of P4. D. Resolution Counterpart of P5. E. Resolution Counterpart of P*3. F. Resolution Counterpart of PS. References. Index. Index of Symbols.

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Book SynopsisI Standard Proof Systems.- A Contraction-free Sequent Calculus for S4.- Transfer of Sequent Calculus Strategies to Resolution for S4.- A Linear Approach to Modal Proof Theory.- Refutations and Proofs in S4.- II Extended Formalisms.- Relational Proof Systems for Modal Logics.- The Display Problem.- Power and Weakness of the Modal Display Calculus.- A Proof-theoretic Proof of Functional Completeness for Many Modal and Tense Logics.- On the Completeness of Classical Modal Display Logic.- Modal Sequents.- Modal Functional Completeness.- A Computational Interpretation of Modal Proofs.- Gabbay-style Calculi.- III Translation-based Proof Systems.- Translating Graded Modalities into Predicate Logics.- From Classical to Normal Modal Logics.Table of ContentsPreface. Part I: Standard Proof Systems. 1. A Contraction-free Sequent Calculus for S4; J. Hudelmaier. 2. Transfer of Sequent Calculus Strategies to Resolution for S4; G. Mints, et al. 3. A Linear Approach to Modal Proof Theory; H. Schellinx. 4. Refutations and Proofs in S4; T. Skura. Part II: Extended Formalisms. 5. Relational Proof Systems for Modal Logics; E. Orlowska. 6. The Display Problem; N. Belnap. 7. Power and Weakness of the Modal Display Calculus; M. Kracht. 8. A Proof-Theoretic Proof of Functional Completeness for Many Modal and Tense Logics; H. Wansing. 9. On the Completeness of Classical Modal Display Logic; R. Goré. 10. Modal Sequents; C. Cerrato. 11. Modal Functional Completeness; K. Dosen, Z. Petric. 12. A Computational Interpretation of Modal Proofs; S. Martini, A. Masini. 13. Gabbay-Style Calculi; S. Mikulás. Part III: Translation-Based Proof Systems. 14. Translating Graded Modalities into Predicate Logic; H.J. Ohlbach, et al. 15. From Classical to Normal Modal Logics; O. Gasquet, A. Herzig.

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Book Synopsis(In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years.Table of ContentsPreface. Part A: Semigroups with Certain Types of Subsemigroup Lattices. I. Preliminaries. II. Semigroups with Modular or Semimodular Subsemigroup Lattices. III. Semigroups with Complementable Subsemigroups. IV. Finiteness Conditions. V. Inverse Semigroups with Certain Types of Lattices of Inverse Subsemigroups. VI. Inverse Semigroups with Certain Types of Lattices of Full Inverse Subsemigroups. Part B: Properties of Subsemigroup Lattices. VII. Lattice Characteristics of Classes of Semigroups. VIII. Embedding Lattices in Subsemigroup Lattices. Part C: Lattice Isomorphisms. IX. Preliminaries on Lattice Isomorphisms. X. Cancellative Semigroups. XI. Commutative Semigroups. XII. Semigroups Decomposable into Rectangular Bands. XIII. Semigroups Defined by Certain Presentations. XIV. Inverse Semigroups. Bibliography. Index. List of Notations. List of Subsections Containing Unsolved Problems or Open Questions.

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Book Synopsis: - the Center for Quantum Philosophy, - the Wealth Creation and Sustainable Development Group, - the Neural Science Group.Table of ContentsPreface; A. Driessen, A. Suarez. Introduction; A. Driessen, A. Suarez. Part I: Mathematics and Undecidability. I. How Can or Should the Recent Developments in Mathematics Influence the Philosophy of Mathematics? H.C. Reichel. II. Number and Randomness, Algorithmic Information Theory - New Results on the Foundations of Mathematics; G.J. Chaitin. III. Meaning, Reality and Algorithms: Implications of the Turing Theorem; F. Cacace. IV. The Limits of Mathematical Reasoning; A. Suarez. V. Mathematics: A Pointer to an Independent Reality, Penrose's Interpretation of the Gödel and Turing Theorems; J.M. Schins. Part II: Physics and Nonlocality. VI. A Critical Approach to Complexity and Self Organization; F.T. Arecchi. VII. Indeterminism and Nonlocality; J.S. Bell. VIII. Nonlocality and the Principle of Free Experimentation; P. Pliska. IX. Optical Tests of Bell's Theorem; A.M. Fox. X. Nonlocal Phenomena: Physical Explanation and Philosophical Implications; A. Suarez. XI. Quantum Theory: A Pointer to an Independent Reality, a Discussion of Bernard d'Espagnat's `Veiled Reality'; J.M. Schins. Part III: Science, Meta-Science and the Existence of God. XII. Scientism and Scientific Knowledge of Things and God; J. Laeuffer. XIII. Physics and the Mind of God; P. Davies. XIV. The Question of the Existence of God in the Book of Stephen Hawking: A Brief History of Time; A. Driessen. XV. Final Remarks: Becoming Aware of Our Fundamental Limits in Knowing and Doing, Implications for the Question of theExistence of God; A. Driessen, A. Suarez. Notes on Contributors. Index.

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Book SynopsisModal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. This book treats multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic.Table of ContentsPreface. 1. Multi-Dimensional Modal Logic. 2. Two- Dimensional Modal Logics. 3. Arrow Logic. 4. Modal Logics of Intervals. 5. Modal Logics of Relations. 6. Multi-Dimensional Semantics for Every Modal Language. Open Problems. A. Modal Similarity Types. B. A Modal Toolkit. Bibliography. List of Symbols. Index.

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Book SynopsisThe conference on Ordered Algebraic Structures held in Curat;ao, from the 26th of June through the 30th of June, 1995, at the Avila Beach Hotel, marked the eighth year of ac­ tivities by the Caribbean Mathematics Foundation (abbr.Table of ContentsPreface. A Survey of f-Rings and Some of Their Generalizations; M. Henriksen. Reflections on the Global Dimensions of Rings of Continuous Functions; R.T. Finn. Continuous Ultraproducts; N.L. Alling. Actions on Archimedean Lattice-Ordered Groups with Strong Unit; R.N. Ball, J.N. Hagler. Pointfree Topology and the Spectra of f-Rings; B. Banaschewski. Commutative Singular f-Rings; R.T. Finn, et al. Torsion Classes of Lattice-Ordered Groups with Invariant Radicals; P.F. Conrad, M.R. Darnel. The Automorphism Groups of Hahn Groups; M. Droste, R. Göbel. The Laterally sigma-Complete Reflection of an Archimedean Lattice-Ordered Group; A.W. Hager, J. Martinez. Ax-Kochen-Ershov Principles for Valued and Ordered Vector Spaces; F. Viktor, S. Kuhlmann. Quasi-Normal f-Rings; S. Larson. Rings of Continuous Functions as Real Closed Rings; N. Schwartz. On Universal Words for Automorphism Groups of Linear Orders; L.V. Welch, S.A. Adeleke.

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Book SynopsisThis is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995.Table of ContentsEditorial. President's Address. Section 1: Proof Theory and Categorical Logic. Proof-Theoretical Aspects of Self-Referential Truth; A. Cantini. Free Lattices, Communication and Money Games; A. Joyal. On Methods for Proving Lower Bounds in Propositional Logic; J. Krajícek. On Bounded Set Theory; V.Yu. Sazonov. Section 2: Model Theory, Set Theory and Formal Systems. Infinitary Logic in Finite Model Theory; Ph.G. Kolaitis. Decision Problems for Second-Order Linear Logic; P.D. Lincoln, et al. Comparing the Continuum with the First Two Uncountable Cardinals; S. Todorcevic. Section 3: Recursion Theory and Constructivism. Church's Thesis and Hume's Problem; K.T. Kelly, O. Schulte. The Logic of Functional Recursion; Y.N. Moschovakis. From Higher Order Terms to Circuits; H. Schwichtenberg, K. Stroetman. Computability and Enumerability; R. Soare. Mechanistic Theories in Cognitive Science: The Import of Turing's Thesis; G. Tamburrini. Section 5: Philosophical Logic. Conjoining and Disjoining on Different Levels; E. Casari. Logical Consequence: A Turn in Style; K. Dosen. Applying Normative Rules with Restraint; S.O. Hansson, D. Makinson. Section 10: Philosophy of Logic, Mathematics and Computer Science. What Can We Do `In Principle'? Ch.D. Parsons. Causation, Action, and Counterfactuals; J. Pearl. Symposium 1: Logic and Philosophy of Science: Current Interfaces. Logic and Philosophy of Science: Current Interfaces; T.A.F. Kuipers. Reliable Belief Revision; K.T. Kelly, et al. Explanatory Translation: Beyond Functionalism and Reductionism; V. Rantala. Abductive Reasoning: Logic, VisualThinking, and Coherence; P. Thagard, C. Shelley. Can the Laws of Nature (Physics) be Complete? P. Weingartner. Symposium 4: Logic in Central and Eastern Europe. Logic in Central and Eastern Europe; P. Hájek. Logic in Czechoslovakia and Hungary; L. Bukovský. Mathematical Logic in the Former Soviet Union: Brief History and Current Trends; V.A. Uspensky. Logic in Central and Eastern Europe: Balkan Region; D. Vakarelov. The Postwar Panorama of Logic in Poland; R. Wójcicki. Closing Address. Structure and Perspective: Philosophical Perplexity and Paradox; B.C. van Fraassen. Table of Contents Volume II.

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Book SynopsisBetween the two world wars, Stanislaw Lesniewski (1886-1939), created the famous and important system of foundations of mathematics that comprises three deductive theories: Protothetic, Ontology, and Mereology. In order to combine these two systematically he constructed Protothetic - the system of `first principles'.Table of ContentsEditor's Foreword. I. Nominalism in Poland; P.M. Simons. II. A Survey of Lesniewski's Logic; F.V. Rickey. III. On the Primitive Term of Logistic; A. Tarski. IV. An Investigation of Protothetic; B. Sobocinski. V. St. Lesniewski's Protothetics; J. Slupecki. VI. On the Single Axioms of Protothetic; B. Sobocinski. VII. Axiomatic Inscriptional Syntax. Part II: The Syntax of Protothetic; F.V. Rickey. VIII. Investigations in Protothetic; A. Le Blanc. Protothetic Bibliography.

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Book SynopsisWhile the notion of a null set can be determined uniquely, the notion of a set of "small" measure has a fuzzy character. It is interesting that the notion of fuzzy set and the notion of a set of small measure (described mathematically by so-called small systems) were introduced independently at almost the same time.Table of Contents1. Sets and Fuzzy Sets. 2. Null Sets and Small Systems. 3. Measures on Ordered Spaces. 4. Subadditive Measures. 5. The Kurzweil Integral in Ordered Spaces. 6. Quantum Logics. 7. Fuzzy-Quantum Spaces. 8. Fuzzy Quantum Logics. 9. Probability on MV Algebras. 10. The Entropy of Fuzzy Dynamical Systems. 11. Measurability and Integrability of Multifunctions. Appendix A: D-Posets. Appendix B: Notes on Order Convergence and Order Topology. References. Index.

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Book Synopsis0 Basic Terminology.- 1 Initial Concepts and Properties.- 2 Homomorphisms.- 3 Divisibility Relations.- 4 Intermediate Associativity.- 5 Semigroup Extensions of Partial Operations.- 6 Partial Groupoids of Transformations.- 7 Factorisation of Partial Groupoids.Table of ContentsPreface. Translator's Preface. 0. Basic Terminology. 1. Initial Concepts and Properties. 2. Homomorphisms. 3. Divisibility Relations. 4. Intermediate Associativity. 5. Semigroup Extensions of Partial Operations. 6. Partial Groupoids of Transformations. 7. Factorisation of Partial Groupoids. Bibliography. Index.

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Book SynopsisIdentifies important developments in intensional logic, a branch of logic with applications in linguistics, cognitive science, artificial intelligence, philosophy, and computer science. The main themes of this book are proof theory, descriptive uses, applications, and foundations of intensional logic.Table of ContentsPreface. Modal Quantification over Structured Domains; J. van Benthem, N. Alechina. Modal Logic and Model-Theoretic Syntax; P. Blackburn, W. Meyer-Viol. The Functional Interpretation of Modal Necessity; R.J.G.B. de Queiroz, D.M. Gabbay. Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic; V.V. Rybakov. The Logic of Correct Description; J. Seligman. Modal Logics of Arrows; D. Vakarelov. A Full-Circle Theorem for Simple Tense Logic; H. Wansing. Canonical Formulas for Modal and Superintuitionistic Logics: A Short Outline; M. Zakharyaschev. The Modal Object Calculus and its Interpretation; E.N. Zalta. Name Index. Subject Index.

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Book SynopsisProceedings of the Conference on Nearrings and Nearfield, Hamburg, Germany, July 30-August 6, 1995Table of ContentsInvited Addresses. From Nearrings and Nearfields to K- Loops; H. Karzel. On Non-Zerosymmetric Near-Rings with Minimum Condition; K. Kaarli. Near-Rings of Homogeneous Functions, P3; C.J. Maxson. The Structure of Omega-Groups; S.D. Scott. Ordered Nearfields; H. Wähling. Contributed Papers. Strongly Idempotent Seminearrings and Their Prime Ideal Spaces; J. Ahsan, Liu Zhongkui. A Note on Simple Composition Rings; E. Aichinger. The Cardinalities of the Endomorphism Near-Rings I(G), A(G), and E(G) for all Groups G with |G| Homogeneous Maps; D. Niewieczerzał. Composition Near-Rings; Q.N. Petersen, S. Veldsman. Categories of Near-Rings; G.F. Pilz. The Inner Automorphism Nearrings I(G) on all Nonabelian Groups G of Order |G| ≤ 100; G. Saad, et al. Special Quasigroups and Steiner Systems; J. Shiftar, H. Zeitler. On the Non-Simplicity of a Subring of M(G); A. Speegle. Near-Rings in Connection with Non-Abelian Cohomology of Groups; M. Ştefănescu. On the Salient Properties of Near-Ring Radicals; S. Veldsman.

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Book SynopsisThis Handbook was produced in the style of previous handbook series like the Handbook of Philosoph­ ical Logic, the Handbook of Logic in Computer Science, the Handbook of Logic in Artificial Intelligence and Logic Programming, and can be seen as a companion to them in covering the wide applications of logic and reasoning.Table of ContentsPreface. Probability, Possibility, Belief: Which and Where? P. Smets. Multi-Valued Logics; G. Panti. Fuzzy Logic; V. Novák. The Bayesian Approach; C. Howson. Confirmation Theory; D. Gillies. Possibility Theory: Qualitative and Quantitative Aspects; D. Dubois, H. Prade. Families of Probabilities; H.E. Kyburg, Jr. The Evidentiary Value Model; N.-E. Sahlin, W. Rabinowicz. The Transferable Belief Model for Quantified Belief Representation; P. Smets. Infinitesimal Theories of Uncertainty for Plausible Reasoning; S. Benferhat. Statistical Inference; A.W.F. Edwards. Graphical Models for Probabilistic and Causal Reasoning; J. Pearl. Game Theory; B. Skyrms, P. Vanderschraaf. Psychological Challenges for Normative Models; G. Gigerenzer. Index.

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Book SynopsisThe papers included in the collection deal with all directions of research undertaken by Polish analytic philosophers. Special attention is paid to logic and comparisons with other philosophical movements, particularly with Brentanism, which was one of the sources of the Lvov - Warsaw school.Table of ContentsPreface. Introduction. The Reception of the Lvov-Warsaw School; J. Wolenski. Part I: History and Comparisons. Twardowski's Distinction Between Actions and Products; J. Brandl. On Ajdukiewicz's Empirical Meaning- Rule and Wittgenstein's Defining Criterion; T. Czarnecki. Inspirations and Controversies: From the Letters Between K. Twardowski and A. Meinong; R. Jadczak. The Lvov-Warsaw School - the First School of Non-Positivist Scientific and Analytic Philosophy; W. Krajewski. Women's Contributions to the Achievements of the Lvov-Warsaw School: A Survey; E. Pakszys. Truth-Bearers from Twardowski to Tarski; A. Rojszczak. Twardowski and Husserl on Wholes and Parts; M. Rosiak. The Rationalistic Paradigm of Franz Brentano and Kazimierz Twardowski; E.G. Vinogradov. Lukasiewicz's Interpretation of Aristotle's Concept of Possibility; U. Zeglen. Part II: Lesniewski. De Veritate: Another Chapter. The Bolzano-Lesniewski Connection; A. Betti. Lesniewski's Conception of Logic; R. Poli, M. Libardi. Non-Elementary Exegesis of Twardowski's Theory of Presentation; V.L. Vasiukov. On Some Essential Subsystems of Lesniewski's Ontology and the Equivalence Between the Singular Barbara and the Law of Leibniz in Ontology; T. Waragai. Part III: Philosophy of Language. The Paradox of Grelling and Nelson Presented as a Veridical Observation Concerning Naming; A. Grzegorczyk. Dambska, Quine and the So-Called Empty Names; M. Marsonet. Truth and Time; K. Misiuna. The Postulate of Precision: Its Sense and Its Limits; M. Przelecki. Polish Logic, Language and Philosophy of Language; R. Zuber. Part IV: Logic and the Foundations of Mathematics. The Ajdukiewicz Calculus, Polish Notationand Hilbert-Style Proofs; W. Buszkowski. Jaśkowski and Gentzen Approaches to Natural Deduction and Related Systems; A. Indrzejczak. The Contribution of Polish Logicians to Recursion Theory; R. Murawski. Studying Incompleteness of Information: A Class of Information Logics; E. Orłowska. Part V: Ontology, Epistemology, Philosophy of Science. On Łukasiewicz's Theory of Probability; T. Childers, O. Majer. On What There Is Not &endash; A Vindication of Reism; J. Czerniawski. On the Concept of a Subject of Cognition in Ajdukiewicz's Philosophy; A. Kanik. Induction and Probability in the Lvov-Warsaw School; I. Niiniluoto. Łukasiewicz's Logical Probability and a Puzzle About Conditionalization; T. Placek. Part VI: Logic and Philosophy. Truth as Consensus. A Logical Analysis; K. Kijania-Placek. The Lvov-Warsaw School and the Problem of a Logical Formalism for General Systems Theory; A.I. Uyemov. From Closure-Operatic Deductive Methodology to Non-Standard Alternatives; S.J. Surma. Forgotten and Neglected Solutions of Problems in Philosophical Logic; P. Weingartner. Index of Names.

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Book SynopsisBASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving ultimately aims at the construction of powerful reasoning tools that let us (computer scientists) prove things we cannot prove without the tools, and the tools cannot prove without us.Table of ContentsVolume I: Foundations. Calculi and Methods. Preface; W. Bibel, P.H. Schmitt. Part One: Tableau and Connection Calculi. Introduction; U. Furbach. 1. Analytic Tableaux; B. Beckert, R. Hähnle. 2. Clausal Tableaux; R. Letz. 3. Variants of Clausal Tableaux; P. Baumgartner, U. Furbach. 4. Cuts in Tableaux; U. Egly. 5. Compressions and Extensions; W. Bibel, et al. Part Two: Special Calculi and Refinements. Introduction; U. Petermann. 6. Theory Reasoning; P. Baumgartner, U. Petermann. 7. Unification Theory; F. Baader, K.U. Schulz. 8. Rigid E-Unification; B. Beckert. 9. Sorted Unification and Tree Automata; C. Weidenbach. 10. Dimensions of Types in Logic Programming; G. Meyer, C. Beierle. 11. Equational Reasoning in Saturation-Based Theorem Proving; L. Bachmair, H. Ganzinger. 12. Higher-Order Rewriting and Equational Reasoning; T. Nipkow, C. Prehofer. 13. Higher-Order Automated Theorem Proving; M. Kohlhase. Index. Volume II: Systems and Implementation Techniques. Introduction; T. Nipkow, W. Reif. 1. Structured Specifications and Interactive Proofs with KIV; W. Reif, et al. 2. Proof Theory at Work: Program Development in the Minlog System; H. Benl, et al. 3. Interactive and Automated Proof Construction in Type Theory; M. Strecker, et al. 4. Integrating Automated and Interactive Theorem Proving; W. Ahrendt, et al. PartTwo: Representation and Optimization Techniques. Introduction; J. Siekmann, D. Fehrer. 5. Term Indexing; P. Graf, D. Fehrer. 6. Developing Deduction Systems: The Toolbox Style; D. Fehrer. 7. Specifications of Inference Rules: Extensions of the PTTP Technique; G. Neugebauer, U. Petermann. 8. Proof Analysis, Generalization and Reuse; T. Kolbe, C. Walther. Part Three: Parallel Inference Systems. Introduction; W. Küchlin. 9. Parallel Term Rewriting with PaReDuX; R. Bündgen, et al. 10. Parallel Theorem Provers Based on SETHEO; J. Schumann, et al. 11. Massively Parallel Reasoning; S.-E. Bornscheuer, et al. Part Four: Comparison and Cooperation of Theorem Provers. Introduction; J. Avenhaus. 12. Extension Methods in Automated Deduction; M. Baaz, et al. 13. A Comparison of Equality Reasoning Heuristics; J. Denzinger, M. Fuchs. 14. Cooperating Theorem Provers; J. Denzinger, I. Dahn. Index. Volume III: Applications. Part One: Automated Theorem Proving in Mathematics. Introduction; M. Kohlhase. 1. Lattice-Ordered Groups in Deduction; I. Dahn. 2. Superposition Theorem Proving for Commutative Rings; J. Stuber. 3. How to Augment a Formal System with a Boolean Algebra Component; H.J. Ohlbach, J. Kühler. 4. Proof Planning: A practical Approach to Mechanized Reasoning in Mathematics; M. Kerber. Part Two: Automated Deduction in Software Engineering and hardware Design. Introduction; J. Schum

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Book SynopsisThis Handbook was produced in the style of previous handbook series like the Handbook of Philosophical Logic, the Handbook of Logic in Computer Science, the Handbook of Logic in Artificial Intelligence and Logic Programming, and can be seen as a companion to them in covering the wide applications of logic and reasoning.Table of ContentsIntroduction to Actual and Potential Contradictions; P. Besnard, A. Hunter. Paraconsistent Logics; A. Hunter. Modal Logics for Representing Incoherent Knowledge; J.-J.Ch. Meyer, W. van der Hoek. The Family of Default Logics; T. Schaub. Conditional Logics for Defeasible Reasoning; J.P. Delgrande. Defeasible Logics; P. Geerts, E. Laenens, D. Vermeir. Necessary Conditions for Negation-Operators (with Particular Applications to Paraconsistent Negation); W. Lenzen. A Survey of Paraconsistent Semantics for Logic Programs; C. Viegas Damásio, L. Moniz Pereira. Index.

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Book SynopsisOne / Introduction.- Two / Sequents Generalized.- Three / Display Logic.- Four / Properly Displayable Logics, Displayable Logics and Strong Cut-Elimination.- Five / A Proof-Theoretic Proof of Functional Completeness for Many Modal and Tense Logics.- Six / Modal Tableaux Based on Residuation.- Seven / Strong Cut-Elimination and Labelled Modal Tableaux.- Eight / Tarskian Structured Consequence Relations and Functional Completeness.- Nine / Constructive Negation and the Modal Logic of Consistency.- Ten / Displaying as Temporalizing.- Eleven / Translation of Hypersequents into Display Sequents.- Twelve / Predicate Logics on Display.- Thirteen / Appendix.Table of ContentsPreface. 1. Introduction. 2. Sequents Generalized. 3. Display Logic. 4. Properly Displayable Logics, Displayable Logics and Strong Cut-Elimination. 5. A Proof-Theoretic Proof of Functional Completeness for Many Modal and Tense Logics. 6. Modal Tableaux Based on Residuation. 7. Strong Cut-Elimination and Labelled Modal Tableaux. 8. Tarskian Structured Consequence Relations and Functional Completeness. 9. Constructive Negation and the Modal Logic of Consistency. 10. Displaying as Temporalizing. 11. Translation of Hypersequents into Display Sequents. 12. Predicate Logics on Display. 13. Appendix. Bibliography. Index.

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Book SynopsisOne / Preliminaries.- 1.1 Introduction.- 1.2 A survey of Boolean propositional logic.- 1.3 Boolean predicate calculus.- 1.4 Function symbols; varieties of algebras.- 1.5 Lattices and Boolean algebras.- 1.6 Ordered Abelian groups.- Two / Many-valued propositional calculi.- 2.1 Continuous t-norms and their residua.- 2.2 The basic many-valued logic.- 2.3 Residuated lattices; a completeness theorem.- 2.4 Some additional topics.- Three / ?ukasiewicz propositional logic.- 3.1 Getting ?ukasiewicz logic.- 3.2 MV-algebras; a completeness theorem.- 3.3 Rational Pavelka logic.- Four / Product logic, Gödel logic.- 4.1 Product logic.- 4.2 Gödel logic.- 4.3 Appendix: Boolean logic.- Five / Many-valued predicate logics.- 5.1 The basic many-valued predicate logic.- 5.2 Completeness.- 5.3 Axiomatizing Gödel logic.- 5.4 ?ukasiewicz and product predicate logic.- 5.5 Many-sorted fuzzy predicate calculi.- 5.6 Similarity and equality.- Six / Complexity and undecidability.- 6.1 Preliminaries.- 6.2 ComplexityTrade Review"...Moreover, it can be an excellent guideline for a postgraduate course in fuzzy logic because of its clear and well-organized content. Definitively, an excellent book that we enthusiastically recommend, and that fuzzy and mathematical logic (and probably philosophical logic as well) communities have been waiting for, for a long time." (F. Esteva, L. Godo, International Journal of General Systems, 29:5 (2000)"On whole this book occupies a unique place in the literature on fuzzy sets and fuzzy logic and fills a substantial gap. This is the only existing monograph offering a comprehensive study of triangular norms and their interconnections. Overall the book is very well written and should become the standard reference for triangular norms."(Mathematical Reviews, 2002a)Table of ContentsPreface. 1. Preliminaries. 2. Many-Valued Propositional Calculi. 3. Lukasiewicz Propositional Logic. 4. Product Logic, Gödel Logic. 5. Many-Valued Predicate Logics. 6. Complexity and Undecidability. 7. On Approximate Inference. 8. Generalized Quantifiers and Modalities. 9. Miscellanea. 10. Historical Remarks. References. Index.

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Book SynopsisConstructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it.Table of Contents1. Introduction and Statement of the Problem.- 2. What’s Wrong with Set Theory?.- 3. What’s Wrong with Infinite Quantifiers?.- 4. Abstraction and Idealisation.- 5. What are Constructions?.- 6. Truth and Proof of Logical Formulae.- 7. The Need for a Theory of Constructions.- 8. Theories of Constructions.- 9. Hilbert’s Formalism.- 10. Open-endedness.- 11. Analysis.- 12. Introduction to Part II.- 13. Design of the Term Language.- 14. The Term Language.- 15. From the Term Language to the Expanded Term Language.- 16. The Expanded Term Language.- 17. The Protological Sequent Calculus.- 18. Commentary on the Protological Axioms and Rules.- 19. From Protologic to Expanded Protologic.- 20. Expanded Protologic.- 21. From Expanded Protologic to the Coding of Trees.- 22. The Coding of Trees.- 23. The Expanded Term Language as a Functional Programming Language.- 24. Introduction to Part III.- 25. From the Coding of Trees to Logic.- 26. Logic.- 27. From Logic to the Calculus of Proof Functions.- 28. Calculus of Proof Functions.- 29. From Calculus of Proof Functions to the Logic of Partial Terms.- 30. Logic of Partial Terms.- 31. From Logic of Partial Terms to Heyting Arithmetic.- 32. Heyting Arithmetic.- 33. From Heyting Arithmetic to Peano Arithmetic.- 34. Peano Arithmetic.- 35. Conclusions on Arithmetic.- 36. Introduction to Part IV.- 37. From Expanded Protologic to the Second-Order Coding of Trees.- 38. The Second-Order Coding of Trees.- 39. From the Second-Order Coding of Trees to Second-Order Logic.- 40. Second-Order Logic.- 41. From Second-Order Logic to Second-Order Calculus of Proof Functions.- 42. Second-Order Calculus of Proof Functions.- 43. From Second-Order Calculus of Proof Functions to Second-Order Logic of Partial Terms.- 44. Second-Order Logic of Partial Terms.- 45. From Second-Order Logic of Partial Terms to Second-Order Heyting Arithmetic.- 46. Second-Order Heyting Arithmetic.- 47. From Second-Order Heyting Arithmetic to Second-Order Peano Arithmetic.- 48. Second-Order Peano Arithmetic.- 49. Conclusions on Analysis.- References.- Index of symbols.- Index of axioms, theorems and rules of inference.- Index of names.- Index of topics.

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Book SynopsisRecent years have been blessed with an abundance of logical systems, arising from a multitude of applications. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on.Table of ContentsPreface. Introduction; M. Fitting. Tableau Methods for Classical Propositional Logic; M. D'Agostino. First-Order Tableau Methods; R. Letz. Equality and Other Theories; B. Beckert. Tableaux for Intuitionistic Logics; A. Waaler, L. Wallen. Tableau Methods for Modal and Temporal Logics; R. Goré. Tableau Methods for Substructural Logics; M. D'Agostino, et al. Tableaux for Nonmonotonic Logics; N. Olivetti. Tableaux for Many-valued Logics; R. Hähnle. Implementing Semantic Tableaux; J. Posegga, P. Schmitt. A Bibliography on Analytic Tableaux Theorem Proving; G. Wrightson. Index.

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Book SynopsisLike the journal TOPOl, the TOPOl Library is based on the assumption that philosophy is a lively, provocative, delightful activity, which constantly challenges our inherited habits, painstakingly elaborates on how things could be different, in other stories, in counterfactual situations, in alternative possible worlds.Table of ContentsAcknowledgments. Introduction. 1: Foundations. 1.1. Languages. 1.2. Models. 1.3. Valuations. 2: Developments. 2.1. Validity. 2.2. Entailment. Concluding Remarks. Appendix. References. Index.

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Book SynopsisThe IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science.Table of ContentsPreface. 1. Operations, Collections and Sets within a General Axiomatic Framework; M. Forti, et al. 2. Some Ins and Outs of Indispensability: A Modal-Structural Perspective; G. Hellman. 3. Carnap's Remarks on Impredicative Definitions and the Genericity Theorem; T. Fruchart, G. Longo. 4. Gödel, Turing, and K-Graph Machines; W. Sieg, J. Byrnes. 5. Linear Recurrence Relations are Delta0 Definable; A. Berarducci, B. Intrigila. 6. On Applicative Theories; G. Jäger, et al. 7. The Use of a Logical Principle of Uniform Boundedness in Analysis; U. Kohlenbach. 8. Epsilon-Substitution Method for the Ramified Language and Delta11-Comprehension Rule; G. Mints, S. Tupailo. 9. The Abstract Compactness Theorem Revisited; X. Caicedo. 10. On Sets Enclosed Between a Set and its Double Complement; W. Veldman. 11. Relations. Binary Relations in the Social and Mathematical Sciences; J. Lambek. 12. Basic Logic and the Cube of its Extensions; G. Battilotti, G. Sambin. 13. Some Observations on Noncommutative Substructural Logics; H. Ono. 14. On Predicate Logic as Modal Logic; D. Westerståhl. 15. A First-Order Effect and Modal Propositional Formulas; A Chagrov. 16. Herbrand's Theorem for a Modal Logic; M. Fitting. 17. Intuitionistic Modal Logic; F. Wolter, M. Zakharyaschev. 18. Dynamic Datatructures; H. Jervell. 19. Resolution and the Decision Problem; A. Leitsch. 20. Model Logic, Linear Logic, OptimalLambda-Reduction; S. Guerrini, et al.

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Book Synopsis2. Functors.- 3. Natural Transformations.- 4. Adjunctions.- 5. Comonads.- 6. Cartesian Categories.- Conclusion.- References.Table of ContentsPreface. Introduction. 1. Categories. 2. Functors. 3. Natural Transformations. 4. Adjunctions. 5. Comonads. 6. Cartesian Categories. Conclusion. References. Index.

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Book SynopsisRecursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics.Table of ContentsPreface. Introduction. 1. Recursive Functions. 2. Gödel's Incompleteness Theorems. 3. Decidability Theory. 4. Philosophical Comments. Bibliography. List of Symbols. Index.

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Book SynopsisCertain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail.Trade Review`... impressively broad and far-ranging... written in an accessible and engaging style... The appendix on Gödel's theorems...is clear and easy to follow... a clear and straightforward survey of the conceptual development of mathematics. It is a wonderful addition to the literature...provides an accessible introduction to the subject matter. I recommend it to anyone who has an interest in mathematics and its development.' Philosophia Mathematica, 8:3 (2000) Table of ContentsForeword. Acknowledgements. 1. Numerals and Notation. 2. The Mathematics of Ancient Greece. 3. The Development of the Number Concept. 4. The Evolution of Algebra, I. 5. The Evolution of Algebra, II. 6. The Evolution of Algebra, III. 7. The Development of Geometry, I. 8. The Development of Geometry, II. 9. The Calculus and Mathematical Analysis. 10. The Continuous and the Discrete. 11. The Mathematics of the Infinite. 12. The Philosophy of Mathematics. Appendices. Bibliography. Index of Names. Index of terms.

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Book SynopsisFuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning.Table of ContentsEditorial Preface; D.M. Gabby. Introduction. Part I: Advances in Multiple-valued Logics. The Poincaré Paradox and Non-classical Logics; U. Höhle. Propositional Fuzzy Logics based on Frank t-norms: A comparison; E.P. Klement, M. Navara. A Resolution-based Axiomatisation of `Bold' Propositional Fuzzy Logic; S. Lehmke. How to Make Your Logic Fuzzy: Fibred Semantics and The Weaving of Logics; D.M. Gabbay. Introducing Grade to Some Metalogical Notions; M.K. Chakraborty, S. Basu. Closure Operators, Fuzzy Logic and Constraints; G. Gerla. Part II: Algebraic Aspects of Multiple-valued Logics. Ulam Game, the Logic of MaxSat, and Many-valued Partitions; D. Mundici. A Many-valued Generalisation of the Ultrapower Construction; C.A. Drossos. Gabriel Filters and the Spectrum of an MV-Algebra; P. Karazeris. Conditional States in Finite-valued Logics; A. Di Nola, et al. Conditioning on MV-algebras and Additive Measures - further results; S. Weber. Part III: Advances in Approximate Reasoning. Toward Adequacy Conditions for Inference Schemata in Approximate Reasoning: The Case of the Rule of Syllogism; S. Gottwald. Formal Theories in Fuzzy Logic; V. Novák. A Note on Fuzzy Inference as Deduction; L. Godo, P. Hájek. The Role of Similarity in Fuzzy Reasoning; F. Klawonn. T-indistinguishability Operators and Approximate Reasoning via CRI; D. Boixader, J. Jacas. About Similarity-based Logical Systems; F. Esteva, et al. On Similarity-based Fuzzy Clusterings; H. Thiele. Part IV: Reasoning about Information and Knowledge. Informational Representability: Abstract Models versus Concrete Models; S. Demri, E. Orlowska. From Possibilistic Information toKleene's Strong Multi-valued Logics; G. De Cooman. A Roadmap of Qualitative Independence; D. Dubois, et al. Truth Functionality and Measure-based Logics; L. Boldrin, C. Sossai. Logic Programs with Context-dependent Preferences; G. Brewka. An Overview of Inconsistency-tolerant Inferences in Prioritized Knowledge Bases; S. Benferhat, et al. Index.

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Book Synopsis1 Basic notions.- 2 Chang completeness theorem.- 3 Free MV-algebras.- 4 ?ukasiewicz ?-valued calculus.- 5 Ulam's game.- 6 Lattice-theoretical properties.- 7 MV-algebras and ?-groups.- 8 Varieties of MV-algebras.- 9 Advanced topics.- 10 Further Readings.Trade Review`Meanwhile, a rich structure theory for MV-algebras has been developed, relating them e.g. to l-groups and to nonstandard reals. The present book develops these matters in detail, and gives a coherent presentation of the core results of the last 15 years or so, also adding unpublished material of the authors. For future work on MV-algebras, this monograph will be an indispensable source.' Mathematical Reviews, 2001Table of ContentsIntroduction. 1. Basic notions. 2. Chang completeness theorem. 3. Free MV-algebras. 4. Lukasiewicz INFINITY-valued calculus. 5. Ulam's game. 6. Lattice-theoretical properties. 7. MV-algebras and l-groups. 8. Varieties of MV-algebras. 9. Advanced topics. 10. Further Readings. Bibliography. Index.

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Book SynopsisMathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.Trade Review`The print and paper are of highly quality. Overall it is a rich and thought-provoking contribution to a relatively undeveloped area of research. The philosophy of the growth of mathematical knowledge has few canonical texts as yet. This book may become one.' Philosophia Mathematica, 10:1 (2002)Table of ContentsAcknowledgments. Introduction. Notes on Contributors. Part I: The Question of Empiricism. The Role of Scientific Theory and Empirical Fact in the Growth of Mathematical Knowledge. 1. Knowledge of Functions in the Growth of Mathematical Knowledge; J. Hintikka. Huygens and the Pendulum: From Device to Mathematical Relation; M.S. Mahoney. 2. An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics; D. Gillies. The Mathematization of Chance in the Middle of the 17th Century; I. Schneider. Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider; M. Liston. 3. The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge; E. Grosholz. Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations; C. Fraser. 4. On Mathematical Explanation; P. Mancosu. Mathematics and the Reelaboration of Truths; F. de Gandt. 5. Penrose and Platonism; M. Steiner. On the Mathematics of Spilt Milk; M. Wilson. Part II: The Question of Formalism. The Role of Abstraction, Analysis, and Axiomatization in the Growth of Mathematical Knowledge. 1. The Growth of Mathematical Knowledge: An Open World View; C. Cellucci. Controversies about Numbers and Functions; D. Laugwitz. Epistemology, Ontology, and the Continuum; C. Posy. 2. Tacit Knowledge and Mathematical Progress; H. Breger. The Quadrature of Parabolic Segments 1635-1658: A Response to Herbert Breger; M.M. Muntersbjorn. Mathematical Progress: Ariadne's Thread; M. Liston. Voir-Dire in the Case of Mathematical Progress; C. Mclarty. 3. The Nature of Progress in Mathematics: The Significance of Analogy; H. Sinaceur. Analogy and the Growth of Mathematical Knowledge; E. Knobloch. 4. Evolution of the Modes of Systematization of Mathematical Knowledge; A. Barabashev. Geometry, the First Universal Language of Mathematics; I. Bashmakova, G.S. Smirnova. Part II: The Question of Progress. Criteria for and Characterizations of Progress in Mathematical Knowledge. 1. Mathematical Progress; P. Maddy. Some Remarks on Mathematical Progress from a Structuralist's Perspective; M.D. Resnik. 2. Scientific Progress and Changes in Hierarchies of Scientific Disciplines; V. Peckhaus. On the Progress of Mathematics; S. Demidov. Attractors of Mathematical Progress: The Complex Dynamics of Mathematical Research; K. Mainzer. On Some Determinants of Mathematical Progress; C. Thiel.

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Book SynopsisOne of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. The early work on classes of alge­ bras was concerned with showing that one class X of algebraic systems is actually contained in another class F.Table of ContentsPreface. 1. Fundamentals of the theory of finite groups. 2. Classical F-subgroups. 3. Formation Structures of Finite Groups. 4. Algebra of Formations. 5. Supplementary Information on Algebra an Theory of Sets. Bibliography. Index of Subjects. List of Symbols.

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Book SynopsisI.- 1. Basic definitions and properties.- 2. Algebraic aspects.- 3. Construction of t-norms.- 4. Families of t-norms.- 5. Representations of t-norms.- 6. Comparison of t-norms.- 7. Values and discretization of t-norms.- 8. Convergence of t-norms.- II.- 9. Distribution functions.- 10. Aggregation operators.- 11. Many-valued logics.- 12. Fuzzy set theory.- 13. Applications of fuzzy logic and fuzzy sets.- 14. Generalized measures and integrals.- A. Families of t-norms.- A.1 Aczél-Alsina t-norms.- A.2 Dombi t-norms.- A.3 Frank t-norms.- A.4 Hamacher t-norms.- A.5 Mayor-Torrens t-norms.- A.6 Schweizer-Sklar t-norms.- A.7 Sugeno-Weber t-norms.- A.8 Yager t-norms.- B. Additional t-norms.- B.1 Krause t-norm.- B.2 A family of incomparable t-norms.- Reference material.- List of Figures.- List of Tables.- List of Mathematical Symbols.Trade Review"The book is very well written and constitutes a valuable addition to the literature on t-norms and, in general fuzzy reasoning. It presents almost all of the most important developments of fuzzy sets and fuzzy logic by focusing on the central concept of triangular norm. It is divided into two parts and an appendix, which gives a summary of the existing families of t-norms."(Mathematical Reviews, 2002a)Table of ContentsAcknowledgments. Introduction. Notations used in this book. Part I: 1. Basic definitions and properties. 2. Algebraic aspects. 3. Construction of t-norms. 4. Families of t-norms. 5. Representations of t-norms. 6. Comparison of t-norms. 7. Values and discretization of t-norms. 8. Convergence of t-norms. Part II: 9. Distribution functions. 10. Aggregation operators. 11. Many-valued logics. 12. Fuzzy set theory. 13. Applications of fuzzy logic and fuzzy sets. 14. Generalized measures and integrals. Appendix A: Families of t-norms. B: Additional t-norms. Reference material. List of Figures. List of Tables. List of Mathematical Symbols. Bibliography. Index.

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