Completeness (logic)

About: Completeness (logic) is a research topic. Over the lifetime, 1590 publications have been published within this topic receiving 25007 citations. The topic is also known as: syntactically complete & semantically complete.

Ten Years of Hoare's Logic: A Survey—Part I

Abstract: A survey of various results concerning Hoare's approach to proving partial and total correctness of programs is presented. Emphasis is placed on the soundness and completeness issues. Various proof systems for while programs, recursive procedures, local variable declarations, and procedures with parameters, together with the corresponding soundness, completeness, and incompleteness results, are discussed.

Rewrite-based Equational Theorem Proving with Selection and Simplification

Abstract: We present various refutationally complete calculi for first-order clauses with equality that allow for arbitrary selection of negative atoms in clauses. Refutation completeness is established via the use of well-founded orderings on clauses for defining a Herbrand model for a consistent set of clauses. We also formulate an abstract notion of redundancy and show that the deletion of redundant clauses during the theorem proving process preserves refutation completeness. It is often possible to compute the closure of nontrivial sets of clauses under application of non-redundant inferences. The refutation of goals for such complete sets of clauses is simpler than for arbitrary sets of clauses, in particular one can restrict attention to proofs that have support from the goals without compromising refutation completeness. Additional syntactic properties allow to restrict the search space even further, as we demonstrate for so-called quasiHorn clauses. The results in this paper contain as special cases or generalize many known results about Knuth-Bendix-like completion procedures (for equations, Horn clauses, and Horn clauses over built-in Booleans), completion of first-order clauses by clausal rewriting, and inductive theorem proving for Horn clauses.

Games and Full Completeness for Multiplicative Linear Logic

Abstract: We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of {\em history-free} strategy; strong connections are made between history-free strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass et al.

Temporal Logic of Programs

Abstract: Logic and Programs.- Historical Remarks.- Some Concepts and Notions of Classical Logic.- I. Propositional Temporal Logic.- 1. A Language TTA of Propositional Temporal Logic.- 2. Semantics of TTA.- 3. Temporal Logical Laws.- 4. Some Further Temporal Operators.- II. Axiomatization of Propositional Temporal Logic.- 5. The Formal System ?TA.- 6. Completeness of ?TA.- 7. Induction Principles.- III. First-Order Temporal Logic.- 8. First-Order Temporal Languages and Their Semantics.- 9. The Formal System ?TP.- 10. The Principle of Well-Founded Orderings.- 11. Additional Propositional Variables.- IV. Temporal Semantics of Programs.- 12. Programs.- 13. Execution Sequences of Programs.- 14. Program Axioms.- 15. Description of Program Properties.- V. Invariance and Precedence Properties of Programs.- 16. The Basic Invariant Method.- 17. Examples of Applications.- 18. Invariant Methods for Precedence Properties.- 19. Examples of Applications.- VI. Eventuality Properties of Programs.- 20. Fair Execution Sequences.- 21. The Finite Chain Reasoning Method.- 22. The Method of Well-Founded Orderings.- 23. Examples of Applications.- VII. Special Methods for Sequential Programs.- 24. Hoare's Calculus.- 25. The Intermittent Assertion Method.- 26. Examples of Applications.- Bibliographical Remarks.- Appendix: Table of Laws and Rules.- References.

The logic of typed feature structures : with applications to unification grammars, logic programs, and constraint resolution

Abstract: This book develops the theory of typed feature structures, a data structure that generalizes both first-order terms and feature structures of unification-based grammars to include inheritance, typing, inequality, cycles and intensionality The resulting synthesis serves as a logical foundation for grammars, logic programming and constraint-based reasoning systems A logical perspective is adopted which employs an attribute-value description language along with complete equational axiomatizations of the various systems of feature structures At the same time, efficiency concerns are kept in mind and complexity and representability results are provided The application of feature structures to phrase structure grammars is described and completeness results are shown for standard evaluation strategies Definite clause logic programs are treated as a special case of phrase structure grammars Constraint systems are introduced and an enumeration technique is developed for solving arbitrary attribute-value logic constraints This book, with its innovative approach to data structure, will be essential reading for researchers in computational linguistics, logic programming and knowledge representation Its self-contained presentation makes it flexible enough to serve as both a research tool and a text book