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Qualitative research for education: An introduction to theories and methods

Boolean satisfiability is probably the most studied of the combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in electronic design automation (EDA), as well as in artificial intelligence (AI). This study has culminated in the development of several SAT packages, both proprietary and in the public domain (e.g. GRASP, SATO) which find significant use in both research and industry. Most existing complete solvers are variants of the Davis-Putnam (DP) search algorithm. In this paper we describe the development of a new complete solver, Chaff which achieves significant performance gains through careful engineering of all aspects of the search-especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy. Chaff has been able to obtain one to two orders of magnitude performance improvement on difficult SAT benchmarks in comparison with other solvers (DP or otherwise), including GRASP and SATO.

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Chaff: engineering an efficient SAT solver

Sexual Behavior in the Human Male

A general logic program (abbreviated to "program" hereafter) is a set of roles that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) slttmg above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that model as the "meaning of the program, " or Its "declarative semantics. " Ideally, queries directed to the program would be answered in accordance with this model. Recent research indicates that some programs do not have a "satisfactory" total model; for such programs, the question of an appropriate partial model arises. Unfounded sets and well-founded partial models are introduced and the well-founded semantics of a program are defined to be its well-founded partial model. If the well-founded partial model is m fact a total model. it is called the well-founded model. It n shown that the class of programs possessing a total well-founded model properly includes previously studied classes of "stratified" and "locally stratified" programs, The method in this paper is also compared with other proposals in the literature, including Clark's "program completion, " Fitting's and Kunen's 3-vahred interpretations of it, and the "stable models" of Gelfond and Lifschitz.

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The well-founded semantics for general logic programs

Logic Semantics for a Class of Committed-Choice Programs.

The Constraint Logic Programming (CLP) Scheme was introduced by Jaffar and Lassez. The scheme gave a formal framework, based on constraints, for the basic operational, logical and algebraic semantics of an extended class of logic programs. This paper presents for the first time the semantic foundations of CLP in a self-contained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important since almost all CLP systems use an incomplete solver. Third, we give conditions on the (possibly incomplete) solver which ensure that the operational semantics is confluent, that is, has independence of literal scheduling.

The Semantics of Constraint Logic Programs

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable.

Propositional defeasible logic has linear complexity

For applications such as deductive databases employing the Open World Assumption, failed derivations have a lesser importance. In this case, use of the identical equivalences based upon the functional semantics [P] and the logical consequences of P allows the application of two different and powerful tools to reason about programs. In particular, these equivalences seem ideal for discussing the deductive structure of such deductive databases, independent of any particular state of the database of facts.

Equivalences of logic programs

In the literature, unification is often treated as a simple and straightforward matter, even though it is recognized as a deep and fundamental concept. However when a thorough presentation is attempted, it is realized then that the matter is fairly subtle and treacherous. For instance, the notion of most general unifier and its property of being unique up to renaming are open to different interpretations. In fact, there are several approaches to unification based on different mathematical concepts that are not equivalent. We present the alternatives and clarify their relationships. In the process, new results are obtained related to the notions of equation solving, most specific generalization, and constraint solving. This leads to a comprehensive presentation of an elementary theory of unification.

Michael J. Maher

Papers

Logic Semantics for a Class of Committed-Choice Programs.

The Semantics of Constraint Logic Programs

Propositional defeasible logic has linear complexity

Equivalences of logic programs

Chapter 15 – Unification Revisited