Results 1  10
of
10
Open answer set programming with guarded programs
, 2006
"... 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 i ..."
Abstract

Cited by 11 (5 self)
 Add to MetaCart
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 2exptimecompleteness of satisfiability checking in such guarded gPs (GgPs). Bound GgPs are restricted GgPs with exptimecomplete 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, alternationfree µGF, and Datalog lite.
Guarded Open Answer Set Programming with Generalized Literals
 In Fourth International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2006
, 2005
"... 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 particul ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
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. Viaa translation to guarded fixed point logic (µGF), in which satisfiability checking is 2EXPTIMEcomplete, we deduce 2EXPTIMEcompleteness of satisfiability checking in such guarded EPs (GEPs). Bound GEPs are restricted GEPs with EXPTIMEcomplete 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, alternationfree µGF, and Datalog LITE. Finally, we discuss ωrestricted logic programs under an open answer set semantics. 1
Games for UML software design
 In Proceedings of Formal Methods for Components and Objects, FMCO'02, volume 2852 of LNCS
, 2003
"... In this paper we introduce the idea of using games as a driving metaphor for design tools which support designers working in UML. ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
In this paper we introduce the idea of using games as a driving metaphor for design tools which support designers working in UML.
J.C.: Modelchecking games for fixpoint logics with partial order models
 In: Proceedings of CONCUR’09. Volume 5710 of LNCS
, 2009
"... Abstract. We introduce modelchecking games that allow local secondorder power on sets of independent transitions in the underlying partial order models where the games are played. Since the onestep interleaving semantics of such models is not considered, some problems that may arise when using int ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We introduce modelchecking games that allow local secondorder power on sets of independent transitions in the underlying partial order models where the games are played. Since the onestep interleaving semantics of such models is not considered, some problems that may arise when using interleaving semantics are avoided and new decidability results for partial orders are achieved. The games are shown to be sound and complete, and therefore determined. While in the interleaving case they coincide with the local modelchecking games for the µcalculus, Lµ, in a noninterleaving setting they verify properties of Separation Fixpoint Logic (SFL), a logic that can specify in partial orders properties not expressible with Lµ. The games underpin a novel decision procedure for modelchecking all temporal properties of a class of infinite and regular event structures, thus improving previous results in the literature. Keywords: Modal and temporal logics; Modelchecking games; Hintikka game semantics; Partial order models of concurrency; Process algebras. 1
On the expressive power of monadic least fixed point logic. Full version of ICALP’04 paper. Available at http://www.informatik.huberlin.de/ ˜schweika/publications.html
"... Abstract. Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of firstorder logic FO and monadic secondorder logic MSO. In this paper we take a closer look at the expressive power of MLFP. Our results are 1. MLFP can describe graph properties beyond any ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of firstorder logic FO and monadic secondorder logic MSO. In this paper we take a closer look at the expressive power of MLFP. Our results are 1. MLFP can describe graph properties beyond any fixed level of the monadic secondorder quantifier alternation hierarchy. 2. On strings with builtin addition, MLFP can describe at least all languages that belong to the linear time complexity class DLIN. 3. Settling the question whether additioninvariant MLFP? = additioninvariant MSO on finite strings would solve open problems in complexity theory: “= ” would imply that PH = PTIME whereas “6= ” would imply that DLIN 6 = LINH. 1
General Terms
"... Open answer set programming combines the strengths of logic programming (a rulebased presentation and a nonmonotonic semantics) and description logics (open domains). Reasoning under an open answer set semantics is undecidable in general, but decidability can be obtained for particular classes of l ..."
Abstract
 Add to MetaCart
Open answer set programming combines the strengths of logic programming (a rulebased presentation and a nonmonotonic semantics) and description logics (open domains). Reasoning under an open answer set semantics is undecidable in general, but decidability can be obtained for particular classes of logic programs, e.g., for bound guarded programs. In this paper, we show how bound guarded programs are expressive enough to simulate satisfiability checking in a DL with nary roles and nominals, yielding EXPTIMEcompleteness for both the DL reasoning and the reasoning with bound guarded programs under the open answer set semantics. We establish decidability of three query problems (query containment, consistency, and disjointness) for guarded queries by a reduction to bound guarded programs, resulting in an EXPTIME upper bound. Categories and Subject Descriptors
Fixed Point Formulae and Solitaire Games
, 2002
"... The model checking games associated with fixed point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time. We study SolitaireLFP, a fragment of least fixed point logic, whose model checking games are nested soltaire ga ..."
Abstract
 Add to MetaCart
The model checking games associated with fixed point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time. We study SolitaireLFP, a fragment of least fixed point logic, whose model checking games are nested soltaire games. This means that on each strongly connected component of the game, only one player can make nontrivial moves. Winning sets of nested solitaire games can be efficiently computed. The model
Program Search as a Path to Artificial General Intelligence
"... It is difficult to develop an adequate mathematical definition of intelligence. Therefore we consider the general problem of searching for programs with specified properties and we argue, using the ChurchTuring thesis, that it covers the informal meaning of intelligence. The program search algorit ..."
Abstract
 Add to MetaCart
It is difficult to develop an adequate mathematical definition of intelligence. Therefore we consider the general problem of searching for programs with specified properties and we argue, using the ChurchTuring thesis, that it covers the informal meaning of intelligence. The program search algorithm can also be used to optimise its own structure and learn in this way. Thus, developing a practical program search algorithm is a way to create AI. To construct a working program search algorithm we show a model of programs and logic in which specifications and proofs of program properties can be understood in a natural way. We combine it with an extensive parser and show how efficient machine code can be generated for programs in this model. In this way we construct a system which communicates in precise natural language and where programming and reasoning can be effectively automated.