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Bibliografická citace

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0 (hodnocen0 x )
BK
Dordrecht : Springer, c1990
xx, 663 s. ; 23 cm

ISBN 90-277-2245-5 (brož.)
Studies in linguistics and philosophy ; vol. 30
Obsahuje bibliografii na s. 637-642 a rejstřík
000035533
Table of Contents // List of Symbols xv // Preface xix // A SET THEORY 1 // 1 Basic Concepts of Set Theory 3 // 1.1 The concept of a set... 3 // 1.2 Specification of sets... 4 // 1.3 Set-theoretic identity and cardinality... 8 // 1.4 Subsets ... 10 // 1.5 Power sets... 11 // 1.6 Union and intersection... 11 // 1.7 Difference and complement ... 15 // 1.8 Set-theoretic equalities... 17 // Exercises ... 23 // 2 Relations and Functions 27 // 2.1 Ordered pairs and Cartesian products... 27 // 2.2 Relations ... 28 // 2.3 Functions... 30 // 2.4 Composition ... 33 // Exercises ... 36 // 3 Properties of Relations 39 // 3.1 Reflexivity, symmetry, transitivity, and connectedness ... 39 // 3.2 Diagrams of relations... 43 // 3.3 Properties of inverses and complements ... 44 // 3.4 Equivalence relations and partitions ... 45 // 3.5 Orderings... 47 // Exercises ... 51 // 4 Infinities 55 // 4.1 Equivalent sets and cardinality... 55 // 4.2 Denumerability of sets... 58 // 4.3 Nondenumerable sets... 62 // 4.4 Infinite vs. unbounded... 70 // Exercises ... 71 // Appendix A: Set-theoretic Reconstruction of Number Systems 75 // A.l The natural numbers... 75 // A.2 Extension to the set of all integers... 78 // A.3 Extension to the set of all rational numbers... 80 // A.4 Extension to the set of all real numbers... 81 // Review Exercises 83 // ? LOGIC AND FORMAL SYSTEMS 85 // 5 Basic Concepts of Logic and Formal Systems 87 // 5.1 Formal systems and models... 87 // 5.2 Natural languages and formal languages...
91 // 5.3 Syntax and semantics ... 92 // 5.4 About statement logic and predicate logic... 93 // 6 Statement Logic 97 // 6.1 Syntax... 97 // 6.2 Semantics: Truth values and truth tables ... 99 // 6.2.1 Negation ... 99 // 6.2.2 Conjunction...100 // 6.2.3 Disjunction...101 // 6.2.4 The Conditional...102 // 6.2.5 The Biconditional...103 // 6.3 Tautologies, contradictions and contingencies...104 // 6.4 Logical equivalence, logical consequence and laws...108 // 6.5 Natural deduction ... 112 // 6.5.1 Conditional Proof...118 // 6.5.2 Indirect Proof...120 // 6.6 Beth Tableaux ...121 // Exercises ...128 // 7 Predicate Logic 135 // 7.1 Syntax...135 // 7.2 Semantics...140 // 7.3 Quantifier laws and prenex normal form...146 // 7.4 Natural deduction ...152 // 7.5 Beth Tableaux ...163 // 7.6 Formal and informal proofs...168 // 7.7 Informal style in mathematical proofs ...170 // Exercises ...173 // 8 Formal Systems, Axiomatization, and Model Theory 179 // 8.1 The syntactic side of formal systems...179 // 8.1.1 Recursive definitions...179 // 8.2 Axiomatic systems and derivations...183 // 8.2.1 Extended axiomatic systems ...186 // 8.3 Semi-Thue systems...190 // 8.4 Peano’s axioms and proof by induction...192 // 8.5 The semantic side of formal systems: model theory...198 // 8.5.1 Theories and models...198 // 8.5.2 Consistency, completeness, and independence ... 200 // 8.5.3 Isomorphism...202 // 8.5.4 An elementary formal system...204 // 8.5.5 Axioms for ordering relations...206 // 8.5.6 Axioms
for string concatenation ...211 // 8.5.7 Models for Peano’s axioms ...214 // 8.5.8 Axiomatization of set theory ...215 // 8.6 Axiomatizing logic...217 // 8.6.1 An axiomatization of statement logic...217 // 8.6.2 Consistency and independence proofs ...220 // 8.6.3 An axiomatization of predicate logic...223 // 8.6.4 About completeness proofs...225 // 8.6.5 Decidability...227 // 8.6.6 Gödel’s incompleteness theorems...228 // 8.6.7 Higher-order logic ...229 // Exercises ...232 // Appendix B-I: Alternative Notations and Connectives 237 // Appendix B-II: Kleene’s Three-Valued Logic 239 // Review Exercises 243 // C ALGEBRA 245 // 9 Basic Concepts of Algebra 247 // 9.1 Definition of algebra...247 // 9.2 Properties of operations...248 // 9.3 Special elements ...249 // 9.4 Maps and morphisms...251 // Exercises ...253 // 10 Operational Structures 255 // 10.1 Groups...255 // 10.2 Subgroups, semigroups and monoids...261 // 10.3 Integral domains...264 // 10.4 Morphisms ...269 // Exercises ...271 // 11 Lattices 275 // 11.1 Posets, duality and diagrams...275 // 11.2 Lattices, semilattices and sublattices...278 // 11.3 Morphisms in lattices ...283 // 11.4 Filters and ideals...285 // 11.5 Complemented, distributive and modular lattices...288 // Exercises ...293 // 12 Boolean and Heyting Algebras 295 // 12.1 Boolean algebras...295 // 12.2 Models of BA...298 // 12.3 Representation by sets...299 // 12.4 Heyting algebra...301 // 12.5 Kripke semantics...304 // Exercises ...307 // Review Exercises 309
// D ENGLISH AS A FORMAL LANGUAGE 313 // 13 Basic Concepts 315 // 13.1 Compositionality...315 // 13.1.1 A compositional account of statement logic...317 // 13.1.2 A compositional account of predicate logic...321 // 13.1.3 Natural language and compositionality...331 // 13.2 Lambda abstraction...336 // 13.2.1 Type theory...336 // 13.2.2 The syntax and semantics of A-abstraction ...339 // 13.2.3 A sample fragment...341 // 13.2.4 The lambda calculus...346 // 13.2.5 Linguistic applications...349 // Exercises ...365 // 14 Generalized Quantifiers 371 // 14.1 Determiners and quantifiers...371 // 14.2 Conditions on quantifiers ...373 // 14.3 Properties of determiners and quantifiers...378 // 14.4 Determiners as relations...388 // 14.5 Context and quantification ...392 // Exercises ...397 // 15 Intensionality 401 // 15.1 Frege’s two problems...401 // 15.2 Forms of opacity...407 // 15.3 Indices and accessibility relations...412 // 15.4 Tense and time...421 // 15.5 Indexicality...425 // Exercises ...427 // E LANGUAGES, GRAMMARS, AND AUTOMATA 429 // 16 Basic Concepts 431 // 16.1 Languages, grammars and automata...431 // 16.2 Grammars...435 // 16.3 Trees...437 // 16.3.1 Dominance...438 // 16.3.2 Precedence...439 // 16.3.3 Labeling...441 // 16.4 Grammars and trees...444 // 16.5 The Chomsky Hierarchy...448 // 16.6 Languages and automata ...451 // 17 Finite Automata, Regular Languages and Type 3 Grammars453 // 17.1 Finite automata ...453 // 17.1.1 State diagrams of finite automata...455 // 17.1.2 Formal
definition of deterministic finite automata . . . 455 // 17.1.3 Non-deterministic finite automata...458 // 17.1.4 Formal definition of non-deterministic finite automata 460 // 17.1.5 Equivalence of deterministic and non-deterministic finite automata...460 // 17.2 Regular languages ...462 // 17.2.1 Pumping Theorem for fal’s...468 // 17.3 Type 3 grammars and finite automaton languages ...471 // 17.3.1 Properties of regular languages...475 // 17.3.2 Inadequacy of right-linear grammars for natural languages ...477 // Exercises ...480 // 18 Pushdown Automata, Context Free Grammars and Languages 485 // 18.1 Pushdown automata...485 // 18.2 Context free grammars and languages...490 // 18.3 Pumping Theorem for cfl’s...492 // 18.4 Closure properties of context free languages...495 // 18.5 Decidability questions for context free languages ...498 // 18.6 Are natural languages context free?...501 // Exercises ...503 // 19 Turing Machines, Recursively Enumerable Languages and // Type 0 Grammars 505 // 19.1 Turing machines ...505 // 19.1.1 Formal definitions...’ . . 508 // 19.2 Equivalent formulations of Turing machines...512 // 19.3 Unrestricted grammars and Turing machines ...513 // 19.4 Church’s Hypothesis...515 // 19.5 Recursive versus recursively enumerable sets...517 // 19.6 The universal Turing machine...518 // 19.7 The Halting Problem for Turing machines...520 // Exercises ...523 // 20 Linear Bounded Automata, Context Sensitive Languages // and Type 1 Grammars 527 // 20.1 Linear
bounded automata... 527 // 20.1.1 Lba’s and context sensitive grammars...528 // 20.2 Context sensitive languages and recursive sets...529 // 20.3 Closure and decision properties...531 // Exercises ...532 // 21 Languages Between Context Free and Context Sensitive 533 // 21.1 Indexed grammars...534 // 21.2 Tree adjoining grammars...540 // 21.3 Head grammars...546 // 21.4 Categorial grammars...547 // 22 Transformational Grammars 553 // Appendix E-I: The Chomsky Hierarchy 559 // Appendix E-II: Semantic Automata 563 // Exercises ...570 // Review Exercises 571 // Solutions to Selected Exercises 573 // Chapter 1...573 // Chapter 2... 575 // Chapter3 . ...576 // Chapter 4...577 // Review problems, Part A ...579 // Chapter 6...582 // Chapter 7...587 // Chapter 8...594 // Review problems, Part ? ...597 // Chapter 9...601 // Chapter 10...602 // Chapter 11 ...606 // Chapter 12...608 // Review problems, Part C ...610 // Chapter 13...614 // Chapter 14...616 // Chapter 15...619 // Chapter 17...620 // Chapter 18...626 // Chapter 19...629 // Chapter 20 ... 630 // Appendix E-II ...631 // Review problems, Part E ...632 // Bibliography 635 // Index // 647

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