301,801 research outputs found
Rewriting recursive aggregates in answer set programming: back to monotonicity
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since the evaluation of normal programs with monotone aggregates is in general on a lower complexity level than the evaluation of normal programs with arbitrary aggregates, any faithful translation function must introduce disjunction in rule heads in some cases. However, no function of this kind is known. The paper closes this gap by introducing a polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers. A prototype system allows for experimenting with arbitrary recursive aggregates, which are also supported in the recent version 4.5 of the grounder gringo, using the methods presented in this paper
An Answer Set Solver for non-Herbrand Programs: Progress Report
In this paper we propose an extension of Answer Set Programming (ASP) by non-Herbrand functions, i.e. functions over non-Herbrand domains, and describe a solver for the new language. Our approach stems for our interest in practical applications, and from the corresponding need to compute the answer sets of programs with non-Herbrand functions efficiently. Our extension of ASP is such that the semantics of the new language is obtained by a comparatively small change to the ASP semantics from [8]. This makes it possible to modify a state-of-the-art ASP solver in an incremental fashion, and use it for the computation of the answer sets of (a large class of) programs of the new language. The computation is rather efficient, as demonstrated by our experimental evaluation
First-Order Stable Model Semantics with Intensional Functions
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 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.Comment: 69 page
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