Logic, meaning and computation : essays in memory of Alonzo Church
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書誌事項
Logic, meaning and computation : essays in memory of Alonzo Church
（Synthese library, v. 305）
Kluwer Academic Publishers, c2001
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Alonzo Church was undeniably one ofthe intellectual giants of theTwenti- eth Century . These articles are dedicated to his memory and illustrate the tremendous importance his ideas have had in logic , mathematics, comput er science and philosophy . Discussions of some of thesevarious contributions have appeared in The Bulletin of Symbolic Logic, and th e interested reader is invited to seek details there . Here we justtry to give somegener al sense of the scope, depth,and value of his work. Church is perhaps best known for the theorem , appropriately called " C h u r c h ' s Theorem ", that there is no decision procedure forthelogical valid- ity of formulas first-order of logic . A d ecision proce dure forthat part of logic would have come near to fulfilling Leibniz's dream of a calculus that could be mechanically used tosettle logical disputes . It was not to . be It could not be . What Church proved precisely is that there is no lambda-definable function that can i n every case providethe right answer , ' y e s ' or ' n o', tothe question of whether or not any arbitrarily given formula is valid .
目次
- Preface
- C.A. Anderson, M. Zeleny. Remembering Alonzo Church
- D. Kaplan, T. Burge. Part I: Logic. Logic, truth and number: The elementary genesis of arithmetic
- P. Apostoli. Second-order logic
- J. Corcoran. A representation of relation algebras using Routley-Meyer frames
- J.M. Dunn. Church's set theory with a universal set
- Th. Forster. Axioms of infinity in Church's type theory
- R.O. Gandy. Logical objects
- E.L. Keenan. The lambda calculus and adjoint functors
- S.M. Lane. Atomic Boolean algebras and classical propositional logic
- G.J. Massey. Improved decision procedures for pure relevant logic
- R.K. Meyer. The `triumph' of first-order languages
- S. Shapiro. Equivalence relations and groups
- R. Smullyan. Part II: Computation. Discriminating coded lambda terms
- H. Barendregt. lambda-calculus as a foundation for mathematics
- K. Grue. Peano's lambda calculus: The functional abstraction implicit in arithmetic
- D. Leivant. The undecidability of lambda-definability
- R. Loader. A construction of the provable wellorderings of the theory of species
- P. Martin-Loef. Semantics for first and higher order realizability
- C. Mclarty. Language and equality theory in logic programming
- J.C. Shepherdson. Part III: Philosophy, Meaning, and Intensional Logic. Alternative (1*): A criterion of identity for intensional entities
- C.A. Anderson. Nominalist paraphrase and ontological commitment
- J.P. Burgess. Peace, justice and computation: Leibniz' program and the moral and political significance of Church's theorem
- M. Detlefsen. Tarski's theorem and NFU
- M.R. Holmes. Church's theorem and randomness
- G. Mar. Russellian type theory andsemantical paradoxes
- E. Martino. The logic of sense and denotation: Extensions and applications
- T. Parsons. Analysis, synonymy and sense
- M. Richard. The very possibility of language
- N. Salmon. Index.
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