Logic: Mathematics, Language, Computer Science and Philosophy

H. C. M. de Swart

ISBN 10: 363145435X / ISBN 13: 9783631454350

Published by Peter Lang, 1994

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -In Logic Programming ( 25 and 26) the language of logic is used as a declarative programming language. Prolog uses resolution as its underlying proof mechanism. The logical structure of relational databases is explained ( 27) in set theoretical terms and it is shown how the language of set theory can be used as a Structured Query Language (SQL). Computability, Undecidability and Complexity are treated in sections 28, 29, and 30, respectively, in terms of Turing machines. The undecidability of the validity problem for predicate logic and the NP-completeness of the satisfiability problem for propositional logic are shown in a similiar way. Chomsky's notion of grammar and its relation to the notion of automation is presented in section 31. Both untyped and typed lambda calculus are treated in sections 32 and 33, respectively. The role epistemic logic can play in the description of distributed systems is explained ( 34). In section 35 and 36, temporal logic is used both for verification by hand and for automatic verification. A tableaux-based automated theorem prover for classical logic is elaborated in the Appendix. Each section ends with a number of exercises; the answers can be found at the end of this book. 337 pp. Englisch.

Seller Inventory # 9783631454350

Bibliographic Details

• Title: Logic: Mathematics, Language, Computer Science and Philosophy
• Publisher: Peter Lang
• Publication Date: 1994
• Language: English
• ISBN 10: 363145435X
• ISBN 13: 9783631454350
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

In Logic Programming ( 25 and 26) the language of logic is used as a declarative programming language. Prolog uses resolution as its underlying proof mechanism. The logical structure of relational databases is explained ( 27) in set theoretical terms and it is shown how the language of set theory can be used as a Structured Query Language (SQL). Computability, Undecidability and Complexity are treated in sections 28, 29, and 30, respectively, in terms of Turing machines. The undecidability of the validity problem for predicate logic and the NP-completeness of the satisfiability problem for propositional logic are shown in a similiar way. Chomsky's notion of grammar and its relation to the notion of automation is presented in section 31. Both untyped and typed lambda calculus are treated in sections 32 and 33, respectively. The role epistemic logic can play in the description of distributed systems is explained ( 34). In section 35 and 36, temporal logic is used both for verification by hand and for automatic verification. A tableaux-based automated theorem prover for classical logic is elaborated in the Appendix. Each section ends with a number of exercises; the answers can be found at the end of this book.

About the Author

The Author: H.C.M. de Swart, born in 1944, studied Mathematics and Physics at Nijmegen University. His Ph.D. thesis was on intuitionistic Logic (1976). He spent the academic year 1976/1977 as a Visiting Fellow at Princeton University. His appointment as professor in Logic and Philosophy of language at Tilburg University followed in 1980. He is author or co-author of several books in Dutch: Sets (1975), Symbolic Logic (1976), Philosophy of Mathematics (1989) and The Theory of Social Choice (1992). He has published in several international journals on, among other subjets, intuitionism, tableaux and orderings.