Logic for Applications

I 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 andFoundation. - 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. Language: English