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Characterizing Boundedness in Chase Variants

THEORY AND PRACTICE OF LOGIC PROGRAMMING 2021年第1期21卷 51-79页

作者： Delivorias, Stathis Leclere, Michel Mugnier, Marie-Laure Ulliana, Federico Univ Montpellier LIRMM CNRS INRIA Montpellier France

Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

关键词： knowledge representation and nonmonotonic reasoning logic programming methodology and applications databases and semantic web reasoning theory

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The Probabilistic Description Logic BALC

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THEORY AND PRACTICE OF LOGIC PROGRAMMING 2021年第4期21卷 404-427页

作者： Botha, Leonard Meyer, Thomas Penaloza, Rafael Univ Cape Town Rondebosch South Africa CAIR Pretoria South Africa Univ Milano Bicocca Milan Italy

Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for representing and handling uncertainty. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the propositionally closed DL ALC. We present a tableau-based procedure for deciding consistency and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC.

关键词： knowledge representation and nonmonotonic reasoning databases and semantic web reasoning

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Introduction to the Special Issue on Logic Rules and reasoning: Selected Papers From the 6th International Joint Conference on Rules and reasoning (RuleML+RR 2022)

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THEORY AND PRACTICE OF LOGIC PROGRAMMING 2025年

作者： Governatori, Guido Turhan, Anni-Yasmin Cent Queensland Univ Brisbane Qld Australia Charles Sturt Univ Sydney NSW Australia Paderborn Univ Paderborn Germany

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Optimizing Answer Set Computation via Heuristic-Based Decomposition

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THEORY AND PRACTICE OF LOGIC PROGRAMMING 2019年第4期19卷 603-628页

作者： Calimeri, Francesco Perri, Simona Zangari, Jessica Univ Calabria Dept Math & Comp Sci Arcavacata Di Rende Italy

Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and non-monotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem;however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones;the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation;we use them in order to implement the approach into the ASP system DLV, in particular into its grounding subsystem I-DLV, and carry out an extensive experimental activity for assessing the impact of the proposal.

关键词： knowledge representation and nonmonotonic reasoning logic programming methodology and applications databases and semantic web reasoning Answer Set Programming

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