M. Fitting's Books

First-Order Modal Logic

By: M. Fitting,Richard L. Mendelsohn

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This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

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Page Count

300

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401152926

ISBN 13

9789401152921

Types, Tableaus, and Gödel’s God

By: M. Fitting

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Types, Tableaus, and Gödel’s God

By: M. Fitting

Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Parts of the book are mathematical, parts philosophical.

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Page Count

190

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401004110

ISBN 13

9789401004114

Fundamentals of Generalized Recursion Theory

By: M. Fitting

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Fundamentals of Generalized Recursion Theory

By: M. Fitting

Fundamentals of Generalized Recursion Theory

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Page Count

329

Publisher

Elsevier

Published Date

ISBN 10

0080960316

ISBN 13

9780080960319

Proof Methods for Modal and Intuitionistic Logics

By: M. Fitting

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Proof Methods for Modal and Intuitionistic Logics

By: M. Fitting

Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.

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Page Count

563

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401727945

ISBN 13

9789401727945

Book's by M. Fitting

First-Order Modal Logic

First-Order Modal Logic

Types, Tableaus, and Gödel’s God

Types, Tableaus, and Gödel’s God

Fundamentals of Generalized Recursion Theory

Fundamentals of Generalized Recursion Theory

Proof Methods for Modal and Intuitionistic Logics

Proof Methods for Modal and Intuitionistic Logics

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