ENGLISH

Logics for Computer Science. Classical and Non-Classical

By Anita Wasilewska

Book information

Publisher
Springer
Year
2018
ISBN
978-3-319-92591-2
Language
english
Format
PDF
Filesize
3 MB (3153329 bytes)
Pages
536\536
Time added
2018-11-11 13:10:37

Description

Contents......Page 3 Mathematical Paradoxes......Page 7 Computer Science Puzzles......Page 13 Homework Problems......Page 18 Intro to Classical Logic......Page 20 Propositional Language......Page 21 Propositional Semantics......Page 26 Examples of Propositional Tautologies......Page 35 Predicate Language Description & Application to Artificial Intelligence......Page 42 Predicate Semantics - Description & Laws of Quantifiers......Page 54 Homework Problems......Page 63 Formal Propositional Languages......Page 69 Extensional Semantics M......Page 79 Classical Semantics......Page 84 Classical Tautologies & Equivalence of Languages......Page 105 Many-valued Semantics - Lukasiewicz, Heyting, Kleene, Bohvar......Page 113 M Tautologies, M Consistency & M Equivalence of Languages......Page 130 Homework Problems......Page 141 General Proof Systems - Syntax & Semantics......Page 148 Syntax......Page 150 Semantics......Page 167 Exercises & Examples......Page 174 Homework Problems......Page 179 Hilbert Proof Systems Completeness of Classical Propositional Logic......Page 181 Deduction Theorem......Page 182 Completeness Theorem - Proof 1......Page 202 Completeness Theorem - Proof 2......Page 213 Other Axiomatizations......Page 224 Exercises......Page 227 Homework Problems......Page 231 Gentzen Style Proof System RS......Page 235 Search for Proofs & Decomposition Trees......Page 243 Strong Soundness & Completeness......Page 254 Proof Systems RS1 & RS2......Page 258 Gentzen Sequent Systems GL, G, LK......Page 265 GL Soundness & Completeness......Page 279 Original Gentzen Systems LK, LI Completeness & Hauptzatz Theorems......Page 285 Homework Problems......Page 304 Intro to Intuitionistic Logic......Page 307 Gentzen Sequent System LI......Page 319 Intro to Modal S4 & S5 Logics......Page 337 Homework Problems......Page 348 Formal Predicate Languages......Page 351 Classical Semantics......Page 366 Predicate Tautologies......Page 382 Hilbert Proof Systems Soundness & Completeness......Page 394 Homework Problems......Page 399 Hilbert Proof Systems Completeness of Classical Predicate Logic......Page 403 Reduction Predicate Logic to Propositional Logic......Page 404 Proof of Completeness Theorem......Page 421 Deduction Theorem......Page 432 Other Axiomatizations......Page 437 Homework Problems......Page 442 Predicate Automated Proof Systems Completeness of Classical Predicate Logic......Page 443 QRS Proof System......Page 444 QRS Decomposition Trees......Page 449 Proof of QRS Completeness......Page 458 Skolemization & Clauses......Page 468 Homework Problems......Page 487 Formal Theories & Gödel Theorems......Page 490 Formal Theories: Definition and Examples......Page 491 PA - Formal Theory of Natural Numbers......Page 501 Consistency, Completeness, Gödel Theorems......Page 516 Proof of the Incompleteness Theorems......Page 527 Homework Problems......Page 535

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