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First-order stable model semantics with intensional functions

ARTIFICIAL INTELLIGENCE 2019年 273卷 56-93页

作者： Bartholomew, Michael Lee, Joohyung Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ 85281 USA

In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order stable model semantics by Ferraris, Lee, and Lifschitz to allow intensional functions-functions that are specified by a logic program just like predicates are specified. We show that many known properties of the stable model semantics are naturally extended to this formalism and compare it with other related approaches to incorporating intensional functions. Furthermore, we use this extension as a basis for defining Answer Set Programming Modulo Theories (ASPMT), analogous to the way that Satisfiability Modulo Theories (SMT) is defined, allowing for SMT-like effective first-order reasoning in the context of Answer Set Programming (ASP). Using SMT solving techniques involving functions, ASPMT can be applied to domains containing real numbers and alleviates the grounding problem. We show that other approaches to integrating ASP and CSP/SMT can be related to special cases of ASPMT in which functions are limited to non intensional ones. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Answer set programming intensional functions Satisfiability modulo theories

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On the stable model semantics for intensional functions

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THEORY AND PRACTICE OF LOGIC PROGRAMMING 2013年第4-5期13卷 863-876页

作者： Bartholomew, Michael Lee, Joohyung Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ 85069 USA

Several extensions of the stable model semantics are available to describe "intensional" functions-functions that can be described in terms of other functions and predicates by logic programs. Such functions are useful for expressing inertia and default behaviors of systems, and can be exploited for alleviating the grounding bottleneck involving functional fluents. However, the extensions were defined in different ways under different intuitions. In this paper we provide several reformulations of the extensions, and note that they are in fact closely related to each other and coincide on large syntactic classes of logic programs.

关键词： answer set programming stable models intensional functions

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On the stable model semantics for intensional functions

On the stable model semantics for intensional functions

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29th International Conference on Logic Programming ICLP

作者： Bartholomew, Michael Lee, Joohyung Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ 85069 USA

关键词： answer set programming stable models intensional functions

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