10 research outputs found
Implementing Stable-Unstable Semantics with ASPTOOLS and Clingo
Normal logic programs subject to stable model semantics cover reasoning problems from the first level of polynomial time hierarchy (PH) in a natural way. Disjunctive programs reach one level beyond this, but the access to the underlying NP oracle(s) is somewhat implicit and available for the programmer using the so-called saturation technique. To address this shortcoming, stable-unstable semantics was proposed, making oracles explicit as subprograms having no stable models. If this idea is applied recursively, any level of PH can be reached with normal programs only, in analogy to quantified Boolean formulas (QBFs). However, for the moment, no native implementations of stable-unstable semantics have emerged except via translations toward QBFs. In this work, we alleviate this situation with a translation of (effectively) normal programs that combines a main program with any fixed number of oracles subject to stable-unstable semantics. The result is a disjunctive program that can be fed as input for answer set solvers supporting disjunctive programs. The idea is to hide saturation from the programmer altogether, although it is exploited by the translation internally. The translation of oracles is performed using translators and linkers from the ASPTOOLS collection while Clingo is used as the back-end solver.acceptedVersionPeer reviewe
Efficient Computation of Answer Sets via SAT Modulo Acyclicity and Vertex Elimination.
publishedVersionPeer reviewe
Allen's Interval Algebra Makes the Difference
Allen's Interval Algebra constitutes a framework for reasoning about temporal
information in a qualitative manner. In particular, it uses intervals, i.e.,
pairs of endpoints, on the timeline to represent entities corresponding to
actions, events, or tasks, and binary relations such as precedes and overlaps
to encode the possible configurations between those entities. Allen's calculus
has found its way in many academic and industrial applications that involve,
most commonly, planning and scheduling, temporal databases, and healthcare. In
this paper, we present a novel encoding of Interval Algebra using answer-set
programming (ASP) extended by difference constraints, i.e., the fragment
abbreviated as ASP(DL), and demonstrate its performance via a preliminary
experimental evaluation. Although our ASP encoding is presented in the case of
Allen's calculus for the sake of clarity, we suggest that analogous encodings
can be devised for other point-based calculi, too.Comment: Part of DECLARE 19 proceeding
A Paraconsistent ASP-like Language with Tractable Model Generation
Answer Set Programming (ASP) is nowadays a dominant rule-based knowledge
representation tool. Though existing ASP variants enjoy efficient
implementations, generating an answer set remains intractable. The goal of this
research is to define a new \asp-like rule language, 4SP, with tractable model
generation. The language combines ideas of ASP and a paraconsistent rule
language 4QL. Though 4SP shares the syntax of \asp and for each program all its
answer sets are among 4SP models, the new language differs from ASP in its
logical foundations, the intended methodology of its use and complexity of
computing models.
As we show in the paper, 4QL can be seen as a paraconsistent counterpart of
ASP programs stratified with respect to default negation. Although model
generation of well-supported models for 4QL programs is tractable, dropping
stratification makes both 4QL and ASP intractable. To retain tractability while
allowing non-stratified programs, in 4SP we introduce trial expressions
interlacing programs with hypotheses as to the truth values of default
negations. This allows us to develop a~model generation algorithm with
deterministic polynomial time complexity.
We also show relationships among 4SP, ASP and 4QL
On the Configuration of More and Less Expressive Logic Programs
The decoupling between the representation of a certain problem, i.e., its
knowledge model, and the reasoning side is one of main strong points of
model-based Artificial Intelligence (AI). This allows, e.g. to focus on
improving the reasoning side by having advantages on the whole solving process.
Further, it is also well-known that many solvers are very sensitive to even
syntactic changes in the input. In this paper, we focus on improving the
reasoning side by taking advantages of such sensitivity. We consider two
well-known model-based AI methodologies, SAT and ASP, define a number of
syntactic features that may characterise their inputs, and use automated
configuration tools to reformulate the input formula or program. Results of a
wide experimental analysis involving SAT and ASP domains, taken from respective
competitions, show the different advantages that can be obtained by using input
reformulation and configuration. Under consideration in Theory and Practice of
Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Cross-Translating Answer Set Programs Using the ASPTOOLS Collection
One viable way of implementing answer set programming (ASP) is to compile (ground) logic programs into other formalisms and to use existing solver technology to compute answer sets. In this article, we present an overview of translators used for such compilations, targeting at other solving paradigms such as Boolean satisfiability checking, satisfiability modulo theories, and mixed integer programming. Borrowing ideas from modern compiler design, such translators can be systematically developed in stages so that the details of the target formalism can be incorporated at the last step of the translation. In this way, the resulting translators realize a cross-compilation framework for answer set programs, coined as cross-translation in this article.Peer reviewe