Guarded Open Answer Set Programming

Heymans, Stijn; Nieuwenborgh, Davy Van; Vermeir, Dirk

doi:10.1007/11546207_8

Cited by 19 publications

(29 citation statements)

References 13 publications

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“…Section 3.3), Deliberation RuleML also allows Negation-as-failure, as used in Logic Programming. This Naf RuleML can be parameterized for Answer Set (AS) semantics (subsuming stable model semantics) and for Well-Founded (WF) semantics, using a semantic attribute, negation, on the enclosing Rulebase, whose default value is AS, accommodating RIF-CASPD [HK09].…”

Section: Naf Rulemlmentioning

confidence: 99%

“…However, the W3C Core and BLD Recommendations cover only a fraction of the Web rule space and their very rigor gives existing Web rule languages little room for RIF conformance. The RuleML Initiativewhose symposia have been a forum for RIF advances from its beginning -has thus been co-hosting the development of further ("non-standard extensions" 3 or) RIF dialects such as the Core Answer Set Programming Dialect (RIF-CASPD) [HK09] and Semantic Inferencing on Large Knowledge (SILK) [GDK09], using the flexibility-enhancing Framework for Logic Dialects (RIF-FLD) [BK10b], as well as RIF RuleML sublanguages such as Datalog with equality plus externals (Dlex) [Bol09] and the envisioned Reaction Rule Dialect (RRD).…”

Section: Introductionmentioning

confidence: 99%

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RuleML 1.0: The Overarching Specification of Web Rules

2010

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Section: Naf Rulemlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

RuleML 1.0: The Overarching Specification of Web Rules

2010

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“…[1]. Two variations of this semantics, the open [8] and generalised open answer set [9] semantics, consider non-ground programs and open domains, thereby relaxing the PNA. For the present version of QEL the correspondence to answer sets can be summarised as follows (see [17,18,3]).…”

Section: Relation To Answer Setsmentioning

confidence: 99%

“…The latter definition of answer set has been further studied in [10,11] where the basis of a first-oder programming language, RASPL-1, is described. An alternative approach to a first-order ASP language is developed in [8,7].…”

Section: Introductionmentioning

confidence: 99%

A Revised Concept of Safety for General Answer Set Programs

Cabalar

Pearce

Valverde

2009

Logic Programming and Nonmonotonic Reasoning

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Abstract.Some answer set solvers deal with programs with variables by requiring a safety condition on program rules. This ensures that there is a close relation between the answer sets of the program and those of its ground version. If we move beyond the syntax of disjunctive programs, for instance by allowing rules with nested expressions, or perhaps even arbitrary first-order formulas, new definitions of safety are required. In this paper we consider a new concept of safety for formulas in quantified equilibrium logic where answer sets can be defined for arbitrary first-order formulas. The new concept captures and generalises two recently proposed safety definitions: that of Lee, Lifschitz and Palla (2008) as well as that of Bria, Leone and Faber (2008). We study the main metalogical properties of safe formulas.

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“…In [14], these external manipulations, i.e. not expressible in the language of programs itself, were compiled into fixed point logic (FPL) [11], i.e.…”

Section: Introductionmentioning

confidence: 99%

Guarded Open Answer Set Programming with Generalized Literals

Heymans

Nieuwenborgh

Vermeir

2006

Lecture Notes in Computer Science

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Abstract.We extend the open answer set semantics for programs with generalized literals. Such extended programs (EPs) have interesting properties, e.g. the ability to express infinity axioms -EPs that have but infinite answer sets. However, reasoning under the open answer set semantics, in particular satisfiability checking of a predicate w.r.t. a program, is already undecidable for programs without generalized literals. In order to regain decidability, we restrict the syntax of EPs such that both rules and generalized literals are guarded. Via a translation to guarded fixed point logic (µGF), in which satisfiability checking is 2-EXPTIME-complete, we deduce 2-EXPTIME-completeness of satisfiability checking in such guarded EPs (GEPs). Bound GEPs are restricted GEPs with EXPTIME-complete satisfiability checking, but still sufficiently expressive to optimally simulate computation tree logic (CTL). We translate Datalog LITE programs to GEPs, establishing equivalence of GEPs under an open answer set semantics, alternation-free µGF, and Datalog LITE. Finally, we discuss ω-restricted logic programs under an open answer set semantics.

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Guarded Open Answer Set Programming

Cited by 19 publications

References 13 publications

RuleML 1.0: The Overarching Specification of Web Rules

RuleML 1.0: The Overarching Specification of Web Rules

A Revised Concept of Safety for General Answer Set Programs

Guarded Open Answer Set Programming with Generalized Literals

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