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A logic of nonmonotone inductive definitions
 ACM transactions on computational logic
, 2007
"... Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated i ..."
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Cited by 28 (16 self)
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Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inflationary induction has been formalized in FO(IFP), this paper formalizes the principle of iterated induction in a new logic for NonMonotone Inductive Definitions (IDlogic). The semantics of the logic is strongly influenced by the wellfounded semantics of logic programming. This paper discusses the formalisation of different forms of (non)monotone induction by the wellfounded semantics and illustrates the use of the logic for formalizing mathematical and commonsense knowledge. To model different types of induction found in mathematics, we define several subclasses of definitions, and show that they are correctly formalized by the wellfounded semantics. We also present translations into classical first or second order logic. We develop modularity and totality results and demonstrate their use to analyze and simplify complex definitions. We illustrate the use of the logic for temporal reasoning. The logic formally extends Logic Programming, Abductive Logic Programming and Datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions. Categories and Subject Descriptors:... [...]:... 1.
Specifying and analysing agentbased social institutions using answer set programming
 IN: AAMAS05 WORKSHOP: AGENTS, NORMS AND INSTITUTIONS FOR REGULATED MULTIAGENT SYSTEMS (ANI@REM
, 2006
"... In this paper we discuss the use of the Answer Set Programming paradigm for representing and analysing specifications of agentbased institutions. We outline the features of institutions we model, and describe how they are translated into ASP programs which can then be used to verify properties of t ..."
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Cited by 12 (4 self)
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In this paper we discuss the use of the Answer Set Programming paradigm for representing and analysing specifications of agentbased institutions. We outline the features of institutions we model, and describe how they are translated into ASP programs which can then be used to verify properties of the specifications. We demonstrate the effectiveness of this approach through the institutions of property and exchange.
On the relation between IDlogic and answer set programming
 In Logics in Artificial Intelligence, 9th European Conference (JELIA), volume 3229 of Lecture Notes in Computer Science
, 2004
"... Abstract. This paper is an analysis of two knowledge representation extensions of logic programming, namely Answer Set Programming and IDLogic. Our aim is to compare both logics on the level of declarative reading, practical methodology and formal semantics. At the level of methodology, we put forw ..."
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Cited by 10 (4 self)
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Abstract. This paper is an analysis of two knowledge representation extensions of logic programming, namely Answer Set Programming and IDLogic. Our aim is to compare both logics on the level of declarative reading, practical methodology and formal semantics. At the level of methodology, we put forward the thesis that in many (but not all) existing applications of ASP, an ASP program is used to encode definitions and assertions, similar as in IDLogic. We illustrate this thesis with an example and present a formal result that supports it, namely an equivalence preserving translation from a class of IDLogic theories into ASP. This translation can be exploited also to use the current efficient ASP solvers to reason on IDLogic theories and it has been used to implement a model generator for IDLogic. 1
A Tarskian Informal Semantics for Answer Set Programming ∗
"... In their seminal papers on stable model semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational agent. To the best of our knowledge, theirs is still the only published systematic account of the i ..."
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Cited by 2 (2 self)
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In their seminal papers on stable model semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational agent. To the best of our knowledge, theirs is still the only published systematic account of the intuitive meaning of rules and programs under the stable semantics. In current ASP practice, however, we find numerous applications in which rational agents no longer seem to play any role. Therefore, we propose here an alternative explanation of the intuitive meaning of ASP programs, in which they are not viewed as statements about an agent’s beliefs, but as objective statements about the world. We argue that this view is more natural for a large part of current ASP practice, in particular the socalled GenerateDefineTest programs.