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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 ..."
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Cited by 5 (3 self)
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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. 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. ..."
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In this paper we introduce the idea of using games as a driving metaphor for design tools which support designers working in UML.
On the expressive power of monadic least fixed point logic
 In Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP’04), Lecture Notes in Computer Science
, 2004
"... 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 leve ..."
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Cited by 1 (1 self)
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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 or, equivalently, settling the question whether MLFP? = MSO on finite strings with addition would solve open problems in complexity theory: “= ” would imply that PH = PTIME whereas “�= ” would imply that DLIN � = LINH. Apart from this we give a selfcontained proof of the previously known result that MLFP is strictly less expressive than MSO on the class of finite graphs.
Program Search as a Path to Artificial General Intelligence
"... Summary. 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 ..."
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Summary. 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. 1 Intelligence and the Search for Programs Intelligence is usually observed when knowledge is used in a smart and creative way to solve a problem. Still, it seems that the core of intelligence is neither