Fitting, Melvin 1942
Overview
Works:  29 works in 188 publications in 5 languages and 3,656 library holdings 

Genres:  Handbooks and manuals 
Roles:  Author, Editor 
Classifications:  QA76.9.A96, 511.3 
Publication Timeline
.
Most widely held works by
Melvin Fitting
Firstorder logic and automated theorem proving by
Melvin Fitting(
Book
)
34 editions published between 1990 and 2013 in English and Undetermined and held by 552 WorldCat member libraries worldwide
Propositional logic  Semantic tableaux and resolution  Other propositional proof procedures  Firstorder logic  Firstorder proof procedures  Implementing tableaux and resolution  Further firstorder features  Equality
34 editions published between 1990 and 2013 in English and Undetermined and held by 552 WorldCat member libraries worldwide
Propositional logic  Semantic tableaux and resolution  Other propositional proof procedures  Firstorder logic  Firstorder proof procedures  Implementing tableaux and resolution  Further firstorder features  Equality
Intuitionistic logic, model theory and forcing by
Melvin Fitting(
Book
)
23 editions published between 1968 and 1969 in 4 languages and held by 470 WorldCat member libraries worldwide
23 editions published between 1968 and 1969 in 4 languages and held by 470 WorldCat member libraries worldwide
Computability theory, semantics, and logic programming by
Melvin Fitting(
Book
)
15 editions published between 1986 and 1989 in English and Japanese and held by 375 WorldCat member libraries worldwide
15 editions published between 1986 and 1989 in English and Japanese and held by 375 WorldCat member libraries worldwide
Set theory and the continuum problem by
Raymond M Smullyan(
Book
)
17 editions published between 1996 and 2010 in English and held by 345 WorldCat member libraries worldwide
"This book is intended to provide the reader with a complete foundation in modern set theory: how the subject is axiomatized, what ordinal and cardinal numbers are, what the role of the axiom of choice is, what constructible sets are, what forcing is"Page [iii]
17 editions published between 1996 and 2010 in English and held by 345 WorldCat member libraries worldwide
"This book is intended to provide the reader with a complete foundation in modern set theory: how the subject is axiomatized, what ordinal and cardinal numbers are, what the role of the axiom of choice is, what constructible sets are, what forcing is"Page [iii]
Fundamentals of generalized recursion theory by
Melvin Fitting(
Book
)
19 editions published in 1981 in English and held by 325 WorldCat member libraries worldwide
19 editions published in 1981 in English and held by 325 WorldCat member libraries worldwide
Proof methods for modal and intuitionistic logics by
Melvin Fitting(
Book
)
12 editions published between 1983 and 2010 in English and Undetermined and held by 269 WorldCat member libraries worldwide
"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, nonnormal modal logics (many introduced by Lemmon). We also consider some quasiregular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and firstorder 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
12 editions published between 1983 and 2010 in English and Undetermined and held by 269 WorldCat member libraries worldwide
"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, nonnormal modal logics (many introduced by Lemmon). We also consider some quasiregular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and firstorder 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
Firstorder modal logic by
Melvin Fitting(
Book
)
16 editions published between 1998 and 1999 in English and Undetermined and held by 237 WorldCat member libraries worldwide
Fitting and Mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background. They adopt throughout a threefold approach. Semantically, they use possible world models; the formal proof machinery is tableaus; and full philosophical discussions are provided of the way that technical developments bear on wellknown philosophical problems. The book covers quantification itself, including the difference between actualist and possibilist quantifiers; equality, leading to a treatment of Frege's morning star/evening star puzzle; the notion of existence and the logical problems surrounding it; nonrigid constants and function symbols; predicate abstraction, which abstracts a predicate from a formula, in effect providing a scoping function for constants and function symbols, leading to a clarification of ambiguous readings at the heart of several philosophical problems; the distinction between nonexistence and nondesignation; and definite descriptions, borrowing from both Fregean and Russellian paradigms
16 editions published between 1998 and 1999 in English and Undetermined and held by 237 WorldCat member libraries worldwide
Fitting and Mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background. They adopt throughout a threefold approach. Semantically, they use possible world models; the formal proof machinery is tableaus; and full philosophical discussions are provided of the way that technical developments bear on wellknown philosophical problems. The book covers quantification itself, including the difference between actualist and possibilist quantifiers; equality, leading to a treatment of Frege's morning star/evening star puzzle; the notion of existence and the logical problems surrounding it; nonrigid constants and function symbols; predicate abstraction, which abstracts a predicate from a formula, in effect providing a scoping function for constants and function symbols, leading to a clarification of ambiguous readings at the heart of several philosophical problems; the distinction between nonexistence and nondesignation; and definite descriptions, borrowing from both Fregean and Russellian paradigms
Types, tableaus, and Gödel's God by
Melvin Fitting(
Book
)
12 editions published in 2002 in English and held by 163 WorldCat member libraries worldwide
Gödel's modal ontological argument is the centrepiece 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, semantically and through tableau rules, to produce a modified version of Montague/Gallin intensional logic. Extensionality, rigidity, equality, identity, and definite descriptions are investigated. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Objections to the Gödel argument are examined, including one due to Howard Sobel showing Gödel's assumptions are so strong that the modal logic collapses. It is shown that this argument depends critically on whether properties are understood intensionally or extensionally. Parts of the book are mathematical, parts philosophical. A reader interested in (modal) type theory can safely skip ontological issues, just as one interested in Gödel's argument can omit the more mathematical portions, such as the completeness proof for tableaus. There should be something for everybody (and perhaps everything for somebody)
12 editions published in 2002 in English and held by 163 WorldCat member libraries worldwide
Gödel's modal ontological argument is the centrepiece 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, semantically and through tableau rules, to produce a modified version of Montague/Gallin intensional logic. Extensionality, rigidity, equality, identity, and definite descriptions are investigated. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Objections to the Gödel argument are examined, including one due to Howard Sobel showing Gödel's assumptions are so strong that the modal logic collapses. It is shown that this argument depends critically on whether properties are understood intensionally or extensionally. Parts of the book are mathematical, parts philosophical. A reader interested in (modal) type theory can safely skip ontological issues, just as one interested in Gödel's argument can omit the more mathematical portions, such as the completeness proof for tableaus. There should be something for everybody (and perhaps everything for somebody)
In praise of simple things by
Greer Fitting(
Book
)
1 edition published in 1975 in English and held by 126 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 126 WorldCat member libraries worldwide
Beyond two : theory and applications of multiplevalued logic(
Book
)
10 editions published in 2003 in English and held by 117 WorldCat member libraries worldwide
This volume represents the state of the art for much current research in manyvalued logics. Primary researchers in the field are among the authors. Major methodological issues of manyvalued logics are treated, as well as applications of manyvalued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief
10 editions published in 2003 in English and held by 117 WorldCat member libraries worldwide
This volume represents the state of the art for much current research in manyvalued logics. Primary researchers in the field are among the authors. Major methodological issues of manyvalued logics are treated, as well as applications of manyvalued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief
Incompleteness in the land of sets by
Melvin Fitting(
Book
)
8 editions published in 2007 in English and held by 64 WorldCat member libraries worldwide
8 editions published in 2007 in English and held by 64 WorldCat member libraries worldwide
Kleene's three valued logics and their children by
Melvin Fitting(
Book
)
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
Festschrift on the occasion of Professor Rohit Parikh's 60th birthday(
Book
)
3 editions published in 1999 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1999 in English and held by 2 WorldCat member libraries worldwide
Modalitate si incompletitudine : logica modala ca logica de ordin superior by
Mircea Dumitru(
Book
)
1 edition published in 2001 in Romanian and held by 2 WorldCat member libraries worldwide
1 edition published in 2001 in Romanian and held by 2 WorldCat member libraries worldwide
Festschrift on the occasion of Professor Rohit Parikh's 60th birthday(
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Negation as refutation by
Melvin Fitting(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Intuitionistic logic by
Melvin Fitting(
Book
)
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
A simple propositional S5 tableau system by
Melvin Fitting(
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Intuitionistic logic, model theory and forcing by
Melvin Fitting(
)
1 edition published in 2000 in English and held by 0 WorldCat member libraries worldwide
Provability, Computability and Reflection
1 edition published in 2000 in English and held by 0 WorldCat member libraries worldwide
Provability, Computability and Reflection
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Agriculture Algebra Artificial intelligence Automatic theorem proving Axiomatic set theory Canning and preserving Computable functions Computational linguistics Computer science Continuum hypothesis Data structures (Computer science) Farm life Forcing (Model theory) Gödel, Kurt GodProof, Ontological Incompleteness theorems Intuitionistic mathematics Logic Logic, Symbolic and mathematical Logic design Manyvalued logic Metaphysics Modality (Logic) Model theory Ontology Parikh, Rohit, Philosophy Predicate calculus Proof theory Recursion theory Religion Set theory Wine and wine making
Alternative Names
Fitting, M.
Fitting, M. C.
Fitting, M. C. 1942
Fitting, M. Ch 1942
Fitting, Malvin
Fitting, Mel 1942
Fitting, Melvin
Fitting, Melvin C. 1942
Fitting, Melvin Chris.
Fitting, Melvin Chris 1942
Melvin Fitting logician
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