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On firstorder definability and computability of progression for localeffect actions and beyond.
 In Proc. of IJCAI’09.
, 2009
"... Abstract In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Unfortunately, progression is not firstorder definable in general. Recently, Vassos, Lakemeyer, and Levesque showed that in case actions have only local effects, pr ..."
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Cited by 11 (2 self)
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Abstract In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Unfortunately, progression is not firstorder definable in general. Recently, Vassos, Lakemeyer, and Levesque showed that in case actions have only local effects, progression is firstorder representable. However, they could show computability of the firstorder representation only for a restricted class. Also, their proofs were quite involved. In this paper, we present a result stronger than theirs that for localeffect actions, progression is always firstorder definable and computable. We give a very simple proof for this via the concept of forgetting. We also show firstorder definability and computability results for a class of knowledge bases and actions with nonlocal effects. Moreover, for a certain class of localeffect actions and knowledge bases for representing disjunctive information, we show that progression is not only firstorder definable but also efficiently computable.
A.: Quantified Epistemic Logics for Reasoning about Knowledge in MultiAgent Systems
 Artificial Intelligence
"... ABSTRACT We investigate quantified interpreted systems, a semantics for multiagent systems in which agents can reason about individuals, their properties, and the relationships among them. We analyse a firstorder epistemic language interpreted on this semantics and show soundness and completeness ..."
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Cited by 10 (7 self)
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ABSTRACT We investigate quantified interpreted systems, a semantics for multiagent systems in which agents can reason about individuals, their properties, and the relationships among them. We analyse a firstorder epistemic language interpreted on this semantics and show soundness and completeness of Q.S5n, an axiomatisation for these structures.
Tractable reasoning in firstorder knowledge bases with disjunctive information
 In Proceedings of AAAI2005 and IAAI2005
, 2005
"... Abstract This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduce ..."
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Cited by 4 (1 self)
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Abstract This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduced to the model checking problem for a small number of characteristic models; and second, the model checking problem itself is tractable for formulas with a bounded number of variables. We show this methodology in action for the reasoning service previously proposed by Liu, Lakemeyer and Levesque for dealing with disjunctive information. They show that their reasoning is tractable in the propositional case and decidable in the firstorder case. Here we apply the methodology and prove that the reasoning is also tractable in the firstorder case if the knowledge base and the query both use a bounded number of variables.
Efficient Reasoning in Multiagent Epistemic Logics
"... Abstract. In many applications, agents must reason about what other agents know, whether to coordinate with them or to come out on top in a competitive situation. However in general, reasoning in a multiagent epistemic logic such as Kn has high complexity. In this paper, we look at a restricted clas ..."
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Cited by 3 (0 self)
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Abstract. In many applications, agents must reason about what other agents know, whether to coordinate with them or to come out on top in a competitive situation. However in general, reasoning in a multiagent epistemic logic such as Kn has high complexity. In this paper, we look at a restricted class of knowledge bases that are sets of modal literals. We call these proper epistemic knowledge bases (PEKBs). We show that after a PEKB has been put in prime implicate normal form (PINF), an efficient databaselike query evaluation procedure can be used to check whether an arbitrary query is entailed by the PEKB. The evaluation procedure is always sound and sometimes complete. We also develop a procedure to convert a PEKB into PINF. As well, we extend our approach to deal with introspection. 1
On the expressiveness of Levesque’s normal form
 J. Artif. Intell. Res. (JAIR
"... Levesque proposed a generalization of a database called a proper knowledge base (KB), which is equivalent to a possibly infinite consistent set of ground literals. In contrast to databases, proper KBs do not make the closedworld assumption and hence the entailment problem becomes undecidable. Leves ..."
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Cited by 2 (0 self)
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Levesque proposed a generalization of a database called a proper knowledge base (KB), which is equivalent to a possibly infinite consistent set of ground literals. In contrast to databases, proper KBs do not make the closedworld assumption and hence the entailment problem becomes undecidable. Levesque then proposed a limited but efficient inference method V for proper KBs, which is sound and, when the query is in a certain normal form, also logically complete. He conjectured that for every firstorder query there is an equivalent one in normal form. In this note, we show that this conjecture is false. In fact, we show that any class of formulas for which V is complete must be strictly less expressive than full firstorder logic. Moreover, in the propositional case it is very unlikely that a formula always has a polynomialsize normal form. 1.
G.: Tractable firstorder Golog with disjunctive knowledge bases
 In: Proc. Commonsense 2009
"... While based on the Situation Calculus, current implementations of the agent control language Golog typically avoid offering full firstorder capabilities, but rather resort to the closedworld assumption for the sake of efficiency. On the other hand, realistic applications need to deal with incompl ..."
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Cited by 1 (1 self)
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While based on the Situation Calculus, current implementations of the agent control language Golog typically avoid offering full firstorder capabilities, but rather resort to the closedworld assumption for the sake of efficiency. On the other hand, realistic applications need to deal with incomplete world knowledge including disjunctive information. Recently Liu, Lakemeyer and Levesque proposed the logic of limited belief SL, which lends itself to efficient reasoning in incomplete firstorder knowledge bases. In particular, SL defines levels of belief which limit reasoning by cases in a principled way. In this paper, we propose to apply SLbased reasoning in the context of a Golog system. Central to our approach is a new search operator that finds plans only within a fixed belief level k, and an iterativedeepeningstyle variant where instead of considering plans with increasing length, the belief level k is incremented in each cycle. Thus, not the shortest plans are preferred, but those which are the computationally cheapest to discover.
Tractable Reasoning in FirstOrder Knowledge Bases
"... with Disjunctive Information This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment pr ..."
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with Disjunctive Information This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduced to the model checking problem for a small number of characteristic models; and second, the model checking problem itself is tractable for formulas with a bounded number of variables. We show this methodology in action for the reasoning service previously proposed by Liu, Lakemeyer and Levesque for dealing with disjunctive information. They show that their reasoning is tractable in the propositional case and decidable in the firstorder case. Here we apply the methodology and prove that the reasoning is also tractable in the firstorder case if the knowledge base and the query both use a bounded number of variables.
Tractable Reasoning in FirstOrder Knowledge Bases
"... with Disjunctive Information This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment pr ..."
Abstract
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with Disjunctive Information This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduced to the model checking problem for a small number of characteristic models; and second, the model checking problem itself is tractable for formulas with a bounded number of variables. We show this methodology in action for the reasoning service previously proposed by Liu, Lakemeyer and Levesque for dealing with disjunctive information. They show that their reasoning is tractable in the propositional case and decidable in the firstorder case. Here we apply the methodology and prove that the reasoning is tractable in the firstorder case provided that the knowledge base and the query both use a bounded number of variables. 1
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence Decidable Reasoning in a Logic of Limited Belief with Introspection and Unknown Individuals
"... There are not very many existing logics of belief which have both a perspicuous semantics and are computationally attractive. An exception is the logic SL, proposed by Liu, Lakemeyer, and Levesque, which allows for a decidable and often even tractable form of reasoning. While the language is firsto ..."
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There are not very many existing logics of belief which have both a perspicuous semantics and are computationally attractive. An exception is the logic SL, proposed by Liu, Lakemeyer, and Levesque, which allows for a decidable and often even tractable form of reasoning. While the language is firstorder and hence quite expressive, it still has a number of shortcomings. For one, beliefs about beliefs are not addressed at all. For another, the names of individuals are rigid, that is, their identity is assumed to be known. In this paper, we show how both shortcomings can be overcome by suitably extending the language and its semantics. Among other things, we show that determining the beliefs of a certain kind of fully introspective knowledge bases is decidable and that unknown individuals in the knowledge base can be accommodated in a decidable manner as well. 1