Logic for Applications / Edition 2by Anil Nerode, Richard A. Shore
This textbook provides a first introduction to mathematical logic which is closely attuned to the applications of logic in computer science. In it the authors emphasize the notion that deduction is a form of computation. Whilst all the traditional subjects of logic are covered thoroughly: syntax, semantics, completeness, and compactness; much of the book deals… See more details below
This textbook provides a first introduction to mathematical logic which is closely attuned to the applications of logic in computer science. In it the authors emphasize the notion that deduction is a form of computation. Whilst all the traditional subjects of logic are covered thoroughly: syntax, semantics, completeness, and compactness; much of the book deals with less traditional topics such as resolution theorem proving, logic programming and non-classical logics - modal and intuitionistic - which are becoming increasingly important in computer science. No previous exposure to logic is assumed and so this will be suitable for upper level undergraduates or beginning graduate students in computer science or mathematics.From reviews of the first edition: "... must surely rank as one of the most fruitful textbooks introduced into computer science ... We strongly suggest it as a textbook ..." SIGACT News
Table of ContentsI Propositional Logic.- 1 Orders and Trees.- 2 Propositions, Connectives and Truth Tables.- 3 Truth Assignments and Valuations.- 4 Tableau Proofs in Propositional Calculus.- 5 Soundness and Completeness of Tableau Proofs.- 6 Deductions from Premises and Compactness.- 7 An Axiomatic Approach*.- 8 Resolution.- 9 Refining Resolution.- 10 Linear Resolution, Horn Clauses and PROLOG.- II Predicate Logic.- 1 Predicates and Quantifiers.- 2 The Language: Terms and Formulas.- 3 Formation Trees, Structures and Lists.- 4 Semantics: Meaning and Truth.- 5 Interpretations of PROLOG Programs.- 6 Proofs: Complete Systematic Tableaux.- 7 Soundness and Completeness of Tableau Proofs.- 8 An Axiomatic Approach*.- 9 Prenex Normal Form and Skolemization.- 10 Herbrand’s Theorem.- 11 Unification.- 12 The Unification Algorithm.- 13 Resolution.- 14 Refining Resolution: Linear Resolution.- III PROLOG.- 1 SLD-Resolution.- 2 Implementations: Searching and Backtracking.- 3 Controlling the Implementation: Cut.- 4 Termination Conditions for PROLOG Programs.- 5 Equality.- 6 Negation as Failure.- 7 Negation and Nonmonotonic Logic.- 8 Computability and Undecidability.- IV Modal Logic.- 1 Possibility and Necessity; Knowledge or Belief.- 2 Frames and Forcing.- 3 Modal Tableaux.- 4 Soundness and Completeness.- 5 Modal Axioms and Special Accessibility Relations.- 6 An Axiomatic Approach*.- V Intuitionistic Logic.- 1 Intuitionism and Constructivism.- 2 Frames and Forcing.- 3 Intuitionistic Tableaux.- 4 Soundness and Completeness.- 5 Decidability and Undecidability.- 6 A Comparative Guide.- VI Elements of Set Theory.- 1 Some Basic Axioms of Set Theory.- 2 Boole’s Algebra of Sets.- 3 Relations, Functions and the Power Set Axiom.- 4 The Natural Numbers, Arithmetic and Infinity.- 5 Replacement, Choice and Foundation.- 6 Zermelo-Fraenkel Set Theory in Predicate Logic.- 7 Cardinality: Finite and Countable.- 8 Ordinal Numbers.- 9 Ordinal Arithmetic and Transfinite Induction.- 10 Transfinite Recursion, Choice and the Ranked Universe.- 11 Cardinals and Cardinal Arithmetic.- Appendix A: An Historical Overview.- 1 Calculus.- 2 Logic.- 3 Leibniz’s Dream.- 4 Nineteenth Century Logic.- 5 Nineteenth Century Foundations of Mathematics.- 6 Twentieth Century Foundations of Mathematics.- 7 Early Twentieth Century Logic.- 8 Deduction and Computation.- 9 Recent Automation of Logic and PROLOG.- 10 The Future.- Appendix B: A Genealogical Database.- Index of Symbols.- Index of Terms.
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