Showing papers on "Conjunctive normal form published in 1989"
TL;DR: A method, called Modal Resolution and inspired by Robinson's resolution method for classical logics, is presented and extended to Q, T, S4, epistemic logic, and S5 and a completeness proof technique based on a variant of the tableau method for formulas in some “clausal” form is presented.
98 citations
30 Oct 1989
TL;DR: It is first shown that CNF (conjunctive normal form) satisfiability is PLS-complete, even with simultaneously bounded size clauses and bounded number of occurrences of variables, and this result is used to show that traveling salesman under the k-opt neighborhood is also P LS-complete.
Abstract: A class of local search problems, PLS (polynomial-time local search), as defined by D.S. Johnson et al. (see J. Comput. Syst. Sci., vol.37, no.1, p.79-100 (1988)) is considered. PLS captures much of the structure of NP problems at the level of their feasible solutions and neighborhoods. It is first shown that CNF (conjunctive normal form) satisfiability is PLS-complete, even with simultaneously bounded size clauses and bounded number of occurrences of variables. This result is used to show that traveling salesman under the k-opt neighborhood is also PLS-complete. It is argued that PLS-completeness is the normal behavior of NP-complete problems. >
75 citations
29 citations
01 Dec 1989
TL;DR: Results are reported showing that there is no polynomial time algorithm using only equivalence queries that exactly identifies deterministic finite state acceptors, nondeterministic finiteState acceptor, context free grammars, disjunctive or conjunctive normal form boolean formulas, or μ -formulas.
Abstract: We report results showing that there is no polynomial time algorithm using only equivalence queries that exactly identifies deterministic finite state acceptors, nondeterministic finite state acceptors, context free grammars, disjunctive or conjunctive normal form boolean formulas, or μ -formulas.
28 citations
28 Sep 1989
TL;DR: It is shown that query evaluation of range restricted deductive databases and queries never flounders, and that range restricted is broader than comparable properties found in the literature.
Abstract: We define the range form of deductive databases and queries. We prove that transformation into range form preserves logical equivalence. On the basis of the range form, we define the class of range restricted deductive databases and queries. SLDNF-resolution is used for query evaluation. We show that query evaluation of range restricted deductive databases and queries never flounders, and that range restricted is broader than comparable properties found in the literature.
22 citations
TL;DR: First-order formulas for basic point-set topology definitions and sample lemmas both in first-order logic and in clausal form are presented in an attempt to extend the mathematical range available for exploration with automated theorem-proving programs.
Abstract: In this paper we present first-order formulas for basic point-set topology, in an attempt to extend the mathematical range available for exploration with automated theorem-proving programs. We present topology definitions and sample lemmas both in first-order logic and in clausal form. We then illustrate some of the difficulties of these sample lemmas through a proof of a basic lemma in five parts.
19 citations
TL;DR: The method reduces to solving problems of integervalued linear programming of a special kind of special kind by constructing efficient lower bounds for the complexity of disjunctive normal forms of Boolean functions with a fixed number of zeros.
Abstract: A method is given for constructing efficient lower bounds for the complexity of disjunctive normal forms of Boolean functions with a fixed number of zeros. The method reduces to solving problems of integervalued linear programming of a special kind. Examples are given.
2 citations
03 Jan 1989
TL;DR: It is shown that the basic properties of the typing system with conjunctive types are still true and the type assignment defines the interpretation of terms in a very general class of models of the λ-calculus: the models that are based on an information system, as defined by Scott.
Abstract: The definitions of Conjunctive types and their subtype relation, as introduced by Coppo-Dezani, are extended to consider the conjunction as a partial mapping from pairs of types to types, and the subtype relation as a relation between finite sets of types and types. These extensions basically mean that only conjunctions of compatible types are allowed and that the subtype relation is more like, so to speak, the implication in propositional logic. We show that the basic properties of the typing system with conjunctive types are still true. The terms that have a type are exactly the terms that are convertible to a head normal form and it is possible to characterize the terms with normal form by means of the types that are derivable for them in the system. Furthermore, the type assignment defines the interpretation of terms in a very general class of models of the l-calculus: the models that are based on an information system, as defined by Scott.
2 citations
01 Jan 1989
TL;DR: This chapter looks at some of the particular problems associated with the computational demands of AI, including the frame problem, and the question of efficiency and just what can and cannot be achieved in a given time frame.
Abstract: This chapter looks at some of the particular problems associated with the computational demands of AI. The frame problem is a serious pragmatic problem characteristic of AI and NL, in which we must consider tradeoffs in time and space efficiency relating to storage and recall of information. More generally, we consider the question of efficiency and just what can and cannot be achieved in a given time frame. This is contrasted with the intransigent problems for which no efficacious algorithm can guarantee a solution in any time frame. Heuristics may be used to trade a fast probable solution against the possibility of failure in both these cases.