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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

This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to numerous semantics of logic programs. An appendix addresses the fixedpoints of (possibly non-monotonic) functions that are sandwiched between functions with the same fixedpoints.

A lemma on closures and its application to modularity in logic programming semantics.

The ﬁrst issue of the journal Theory and Practice of Logic Programming, or TPLP, was published in January 2001. This issue, the last one in the present volume, and the following issue, the ﬁrst one in the next volume, comprise a collection of papers com-memorating and celebrating the twentieth anniversary of the journal. This celebratory collection comes with about one year delay due to the COVID-19 pandemic (but also, if we were to be entirely honest, because of a common human tendency to put things oﬀ). Whatever the true reason for the delay, the collection is ﬁnally here. We hope and expect it will prove to be a demonstration of the vitality of logic programming, and of a broad range of research directions it spawned in the past and continues to generate today. Logic programming computer a of research on automated theorem proving in logic the of the programming The these original of inspiration of

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Introduction to the Collection of Papers Celebrating the 20th Anniversary of TPLP

The filtering method considered in this paper is based on approximation of a spatial object in d-dimensional space by the minimal convex polyhedron that encloses the object and whose facets are normal to preselected axes. These axes are not necessarily the standard coordinate axes; furthermore, their number is not determined by the dimension of the space. We optimize filtering by selecting optimal such axes based on a preprocessing analysis of stored objects or a sample thereof. The number of axes selected represents a trade-off between access time and storage overhead, as more axes usually lead to better filtering but require more overhead to store the associated access structures. We address the problem of minimizing the number of axes required to achieve a predefined quality of filtering and the reverse problem of optimizing the quality of filtering when the number of axes is fixed. In both cases we also show how to find an optimal collection of axes. To solve these problems, we introduce and study the key notion of separability classification, which is a general tool potentially useful in many applications of a computational geometry flavor. The approach is best suited to applications in which the spatial data is relatively static, some directions are more dominant than others, and the dimension of the space is not high; maps are a prime example.

Separability of Polyhedra for Optimal Filtering of Spatial and Constraint Data

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.

Rewriting general conjunctive queries using views

We address the problem of compiling defeasible theories to Datalog$^\neg$ programs. We prove the correctness of this compilation, for the defeasible logic $DL(\partial_{||})$, but the techniques we use apply to many other defeasible logics. Structural properties of $DL(\partial_{||})$ are identified that support efficient implementation and/or approximation of the conclusions of defeasible theories in the logic, compared with other defeasible logics. We also use previously well-studied structural properties of logic programs to adapt to incomplete Datalog$^\neg$ implementations.

Michael J. Maher

Papers

A lemma on closures and its application to modularity in logic programming semantics.

Introduction to the Collection of Papers Celebrating the 20th Anniversary of TPLP

Separability of Polyhedra for Optimal Filtering of Spatial and Constraint Data

Rewriting general conjunctive queries using views

Defeasible Reasoning via Datalog$^\neg$