Abstract: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 ge… Show more
restricting the agents to specific procedures (that are known to be norm compliant). Such a mechanism of active norm enforcement ensures a good balance between autonomy and conformity in an institution.
restricting the agents to specific procedures (that are known to be norm compliant). Such a mechanism of active norm enforcement ensures a good balance between autonomy and conformity in an institution.
Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants. We define a fixed point logic (FPL) extension of Clark's completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (µ(L)GF). Moreover, we reduce normal closed ASP to loosely guarded OASP, enabling for the first time, a characterization of an answer set semantics by µLGF formulas.We further extend the open answer set semantics for programs with generalized literals. Such generalized programs (gPs) have interesting properties, e.g., the ability to express infinity axioms. We restrict the syntax of gPs such that both rules and generalized literals are guarded. Via a translation to guarded fixed point logic, we deduce 2-exptime-completeness of satisfiability checking in such guarded gPs (GgPs). Bound GgPs are restricted GgPs with exptime-complete satisfiability checking, but still sufficiently expressive to optimally simulate computation tree logic (CTL). We translate Datalog lite programs to GgPs, establishing equivalence of GgPs under an open answer set semantics, alternation-free µGF, and Datalog lite. This is a revised and extended version of [Heymans et al. 2005a] and [Heymans et al. 2006a].
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