Results 1  10
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34
Tractable reasoning with incomplete firstorder knowledge in dynamic systems with contextdependent actions
 In Proc. of IJCAI
, 2005
"... A basic reasoning problem in dynamic systems is the projection problem: determine if a formula holds after a sequence of actions has been performed. In this paper, we propose a tractable1 solution to the projection problem in the presence of incomplete firstorder knowledge and contextdependent a ..."
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Cited by 27 (6 self)
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A basic reasoning problem in dynamic systems is the projection problem: determine if a formula holds after a sequence of actions has been performed. In this paper, we propose a tractable1 solution to the projection problem in the presence of incomplete firstorder knowledge and contextdependent actions. Our solution is based on a type of progression, that is, we progress the initial knowledge base (KB) wrt the action sequence and answer the query against the resulting KB. The form of reasoning we propose is always logically sound and is also logically complete when the query is in a certain normal form and the agent has complete knowledge about the context of any contextdependent actions. 1
Knowledge Equivalence in Combined Action Theories
 In KR’02
, 2002
"... We investigate the relationship between two accounts of knowledge and action in the situation calculus: the Scherl and Levesque (SL) approach that models knowledge with possible worlds, and the Demolombe and Pozos Parra (DP) approach that models knowledge by a set of “knowledge fluents. ” We constru ..."
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Cited by 18 (6 self)
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We investigate the relationship between two accounts of knowledge and action in the situation calculus: the Scherl and Levesque (SL) approach that models knowledge with possible worlds, and the Demolombe and Pozos Parra (DP) approach that models knowledge by a set of “knowledge fluents. ” We construct combined action theories: basic action theories that encode a correspondence between an SL and a DP theory. We prove, subject to certain restrictions, that knowledge of fluent literals are provably the same after a sequence of actions. Moreover, this knowledge equivalence extends to a rich class of formulae. These results allow us to translate certain SL theories into equivalent DP theories that avoid the computational drawbacks of possible world reasoning. They also enable us to prove the correctness of the DP treatment of knowledge and action in terms of a possible world specification. 1
EvaluationBased Reasoning with Disjunctive Information in FirstOrder Knowledge Bases
 In Proc. of KR02
, 2002
"... In previous work, Levesque proposed an evaluationbased reasoning procedure for socalled proper KBs, equivalent to a possibly incomplete possibly infinite set of functionfree ground literals. The procedure, called V; preserved the efficiency and logical soundness of database query evaluation ..."
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Cited by 13 (7 self)
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In previous work, Levesque proposed an evaluationbased reasoning procedure for socalled proper KBs, equivalent to a possibly incomplete possibly infinite set of functionfree ground literals. The procedure, called V; preserved the efficiency and logical soundness of database query evaluation. Moreover, if the query was constrained to be in a special normal form, V was also logically complete. In this paper, we propose an extension to this work to handle disjunctive information in a KB. We define a query evaluation procedure X that generalizes V to deal with KBs that are equivalent to a possibly infinite set of functionfree ground clauses.
Grounding for model expansion in kguarded formulas with inductive definitions
 In IJCAI
, 2007
"... Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies ..."
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Cited by 12 (6 self)
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Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies a given formula. Their longterm goal is to produce practical tools to solve combinatorial search problems, especially those in NP. In this framework, a problem is encoded in a logic, an instance of the problem is represented by a finite structure, and a solver generates solutions to the problem. This approach relies on propositionalisation of highlevel specifications, and on the efficiency of modern SAT solvers. Here, we propose an efficient algorithm which combines grounding with partial evaluation. Since the MX framework is based on classical logic, we are able to take advantage of known results for the socalled guarded fragments. In the case of kguarded formulas with inductive definitions under a natural restriction, the algorithm performs much better than naive grounding by relying on connections between kguarded formulas and tree decompositions. 1
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.
Conditional independence in propositional logic
, 2002
"... Independence—the study of what is relevant to a given problem of reasoning—is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and some more restricted forms of it. Many characteriz ..."
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Cited by 10 (4 self)
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Independence—the study of what is relevant to a given problem of reasoning—is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and some more restricted forms of it. Many characterizations and properties of these independence relations are provided. We show them related to many other notions of independence pointed out so far in the literature (mainly formulavariable independence, irrelevance and novelty under various forms, separability, interactivity). We identify the computational complexity of conditional independence and of all these related independence relations.
A Logic of Limited Belief for Reasoning with Disjunctive Information
 Proceedings of the 9th International Conference on Principles of Knowledge Representation and Reasoning (KR04
, 2004
"... The goal of producing a general purpose, semantically motivated, and computationally tractable deductive reasoning service remains surprisingly elusive. By and large, approaches that come equipped with a perspicuous model theory either result in reasoners that are too limited from a practical point ..."
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Cited by 9 (6 self)
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The goal of producing a general purpose, semantically motivated, and computationally tractable deductive reasoning service remains surprisingly elusive. By and large, approaches that come equipped with a perspicuous model theory either result in reasoners that are too limited from a practical point of view or fall off the computational cliff. In this paper, we propose a new logic of belief called SL which lies between the two extremes. We show that query evaluation based on SL for a certain form of knowledge bases with disjunctive information is tractable in the propositional case and decidable in the firstorder case. Also, we present a sound and complete axiomatization for propositional SL.
Scaling Up Reasoning About Actions Using Relational Database Technology
"... Reiter's variant of the Situation Calculus is tightly related to relational databases, when complete information on the initial situation is available. In particular, the information on the initial situation can be seen as a relational database, and actions, as specified by the precondition ..."
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Cited by 6 (1 self)
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Reiter's variant of the Situation Calculus is tightly related to relational databases, when complete information on the initial situation is available. In particular, the information on the initial situation can be seen as a relational database, and actions, as specified by the preconditions and successor state axioms, can be seen as operations that change the state of the database. In this paper, we show how to exploit such a correspondence to build systems for reasoning about actions based on standard relational database technology. Indeed, by exploiting standard relational DBMS services, a system may be able to perform both Projection, exploiting DBMS querying services, and Progression, exploiting DBMS update services, in very large action theories. A key result towards such a realization, is that under very natural conditions Reiter's basic action theories turn out to be made of "safe formulas" (where basically negation is used as a form of difference between predicates only) and that regression and progression preserve such a safeness. This is a fundamental property to efficiently exploit relational database technology for reasoning. We then show that, even when action theories are not "safe", they can be made so while trying to retain efficiency as much as possible.
On the complexity of model expansion
 In Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning, LPAR’10
, 2010
"... Abstract. We study the complexity of model expansion (MX), which is the problem of expanding a given finite structure with additional relations to produce a finite model of a given formula. This is the logical task underlying many practical constraint languages and systems for representing and sol ..."
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Cited by 5 (2 self)
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Abstract. We study the complexity of model expansion (MX), which is the problem of expanding a given finite structure with additional relations to produce a finite model of a given formula. This is the logical task underlying many practical constraint languages and systems for representing and solving search problems, and our work is motivated by the need to provide theoretical foundations for these. We present results on both data and combined complexity of MX for several fragments and extensions of FO that are relevant for this purpose, in particular the guarded fragment GFk of FO and extensions of FO and GFk with inductive definitions. We present these in the context of the two closely related, but more studied, problems of model checking and finite satisfiability. To obtain results on FO(ID), the extension of FO with inductive definitions, we provide translations between FO(ID) with FO(LFP), which are of independent interest. 1
Complexity of expanding a finite structure and related tasks
 The 8th Int. Workshop on Logic and Comput. Complexity (LCC
, 2006
"... The authors of [MT05] proposed a declarative constraint programming framework based on classical logic extended with nonmonotone inductive definitions. In the framework, a problem instance is a finite structure, and a problem specification is a formula defining the relationship between an instance ..."
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Cited by 4 (4 self)
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The authors of [MT05] proposed a declarative constraint programming framework based on classical logic extended with nonmonotone inductive definitions. In the framework, a problem instance is a finite structure, and a problem specification is a formula defining the relationship between an instance and its solutions. Thus, problem solving amounts to expanding a finite structure with new relations, to satisfy the formula. We present here the complexities of model expansion for a number of logics, alongside those of satisfiability and model checking. As the task is equivalent to witnessing the existential quantifiers in ∃SO model checking, the paper is in large part of a survey of this area, together with some new results. In particular, we describe the combined and data complexity of FO(ID), firstorder logic extended with inductive definitions [DT04] and the guarded and kguarded logics of [AvBN98] and [GLS01]. 1