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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

Output in CLP.

This paper proposes to specify semantic definitions for logic programming languages such as Prolog in terms of an oracle which specifies the control strategy and identifies which clauses are to be applied to resolve a given goal. The approach is quite general. It can be applied to Prolog to specify both operational and declarative semantics as well as other logic programming languages. Previous semantic definitions for Prolog typically encode the sequential depth-first search of the language into various mathematical frameworks. Such semantics mimic a Prolog interpreter in the sense that following the "leftmost" infinite path in the computation tree excludes computation to the right of this path from being considered by the semantics. The basic idea in this paper is to abstract away from the sequential control of Prolog and to provide a declarative characterization of the clauses to apply to a given goal. The decision whether or not to apply a clause is viewed as a query to an oracle which is specified from within the semantics and reasoned about from outside. This approach results in simple and concise semantic definitions which are more useful for arguing the correctness of program transformations and providing the basis for abstract interpretations than previous proposals.

Oracle Semantics for Prolog

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches.In this paper we establish close links to known semantics of extended logic programs. In particular, we give a translation of a defeasible theory D into a program P(D). We showtha t under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.

Embedding Defeasible Logic into Logic Programs

Representing and reasoning with temporal information is an essential part of many tasks in AI such as scheduling, planning and natural language processing. Two influential frameworks for representing temporal information are interval algebra and point algebra [1, 8]. Given a knowledge-base consisting of temporal relations, the main reasoning problem is to determine whether this knowledge-base is satisfiable, i.e., there is a scenario which is consistent with the information provided. However, when a given set of temporal relations is unsatisfiable, no further reasoning is performed. We argue that many real world problems are inherently overconstrained, and that these problems must also be addressed. This paper investigates approaches for handling overconstrainedness in temporal reasoning. We adapt a well studied notion of partial satisfaction to define partial scenarios or optimal partial solutions. We propose two reasoning procedures for computing an optimal partial solution to a problem (or a complete solution if it exists).

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Solving Overconstrained Temporal Reasoning Problems

The problem of rewriting queries using views has important applications in data integration, query optimization, and physical data independence maintenance. Previous researchers have proposed rewriting algorithms for queries and views that are Datalog programs or conjunctive queries with arithmetic comparisons such as x < y and y ≥ 10. We present a method for finding rewritings of general conjunctive queries, i.e, conjunctive queries with arbitrary built-in predicates, using views. Our method also has advantages over previous algorithms when there are no built-in predicates or when the built-in predicates are conjunctions of arithmetic comparisons. In particular, our method finds strictly more rewritings than the MiniCon [PL00] and the Shared-Variable-Bucket [Mit01] algorithms and tends to be more efficient when the built-in predicates of the query involve only distinguished variables. It finds all rewritings that can be found by the Bucket [LRO96] algorithm in most practical cases, and more efficiently. It finds maximum rewritings in several special cases.

Michael J. Maher

Papers

Output in CLP.

Oracle Semantics for Prolog

Embedding Defeasible Logic into Logic Programs

Solving Overconstrained Temporal Reasoning Problems

Rewriting general conjunctive queries using views