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90
On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals
 ARTIFICIAL INTELLIGENCE
, 1992
"... We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or ..."
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Cited by 190 (11 self)
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We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
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Cited by 116 (26 self)
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This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 complete; analogous results are derived for the an
Propositional Circumscription and Extended Closed World Reasoning are $\Pi^P_2$complete
 Theoretical Computer Science
, 1993
"... Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction prob ..."
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Cited by 99 (21 self)
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Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$complete, and we show how this result applies to other variants of closed world reasoning.
An incremental interpreter for highlevel programs with sensing
 In Logical Foundations for Cognitive Agents, Contributions in Honor of Ray Reiter
, 1999
"... Like classical planning, the execution of highlevel agent programs requires a reasoner to look all the way to a final goal state before even a single action can be taken in the world. This deferral is a serious problem in practice for large programs. Furthermore, the problem is compounded in the pr ..."
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Cited by 95 (10 self)
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Like classical planning, the execution of highlevel agent programs requires a reasoner to look all the way to a final goal state before even a single action can be taken in the world. This deferral is a serious problem in practice for large programs. Furthermore, the problem is compounded in the presence of sensing actions which provide necessary information, but only after they are executed in the world. To deal with this, we propose (characterize formally in the situation calculus, and implement in Prolog) a new incremental way of interpreting such highlevel programs and a new highlevel language construct, which together, and without loss of generality, allow much more control to be exercised over when actions can be executed. We argue that such a scheme is the only practical way to deal with large agent programs containing both nondeterminism and sensing.
The Logic of Knowledge Bases
, 2000
"... Recently Lakemeyer and Levesque proposed the logic, which amalgamates both the situation calculus and Levesque’s logic of only knowing. While very expressive the practical relevance of the formalism is unclear because it heavily relies on secondorder logic. In this paper we demonstrate that the pic ..."
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Cited by 91 (8 self)
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Recently Lakemeyer and Levesque proposed the logic, which amalgamates both the situation calculus and Levesque’s logic of only knowing. While very expressive the practical relevance of the formalism is unclear because it heavily relies on secondorder logic. In this paper we demonstrate that the picture is not as bleak as it may seem. In particular, we show that for large classes of knowledge bases and queries, including epistemic ones, query evaluation requires firstorder reasoning only. We also provide a simple semantic definition of progressing a knowledge base. For a particular class of knowledge bases, adapted from earlier results by Lin and Reiter, we show that progression is firstorder representable and easy to compute. 1
Logical filtering
 In Proc. IJCAI03
, 2003
"... Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing possible world states and the agent has a (possibly nondeterministic) log ..."
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Cited by 43 (7 self)
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Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing possible world states and the agent has a (possibly nondeterministic) logical model of its environment and sensors. This paper presents efficient logical filtering algorithms that maintain a compact belief state representation indefinitely, for a broad range of environment classes including nondeterministic, partially observable STRIPS environments and environments in which actions permute the state space. Efficient filtering is also possible when the belief state is represented using prime implicates, or when it is approximated by a logically weaker formula. 1
Projection using Regression and Sensors
 In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
, 1999
"... In this paper, we consider the projection task (determining what does or does not hold after performing a sequence of actions) in a general setting where a solution to the frame problem may or may not be available, and where online information from sensors may or may not be applicable. We forma ..."
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Cited by 38 (9 self)
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In this paper, we consider the projection task (determining what does or does not hold after performing a sequence of actions) in a general setting where a solution to the frame problem may or may not be available, and where online information from sensors may or may not be applicable. We formally characterize the projection task for actions theories of this sort, and show how a generalized form of regression produces correct answers whenever it can be used. We characterize conditions on action theories, sequences of actions, and sensing information that are sufficient to guarantee that regression can be used, and present a provably correct regressionbased procedure in Prolog for performing the task under these conditions.
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
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Cited by 35 (6 self)
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In this tutorialoverview, which resulted from a lecture course given by the authors at
Heterogeneous Active Agents, I: Semantics
, 1999
"... Over the years, many different agent programming languages have been proposed. In this paper, we propose a concept called Agent Programs using which, the way an agent should act in various situations can be declaratively specified by the creator of that agent. Agent Programs may be built on top o ..."
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Cited by 35 (6 self)
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Over the years, many different agent programming languages have been proposed. In this paper, we propose a concept called Agent Programs using which, the way an agent should act in various situations can be declaratively specified by the creator of that agent. Agent Programs may be built on top of arbitrary pieces of software code and may be used to specify what an agent is obliged to do, what an agent may do, and what an agent may not do. In this paper, we define several successively more sophisticated and epistemically satisfying declarative semantics for agent programs. We further show that agent programs cleanly extend well understood semantics for logic programs, and thus are clearly linked to existing results on logic programming and nonmonotonic reasoning.
On Strongest Necessary and Weakest Sufficient
 Artificial Intelligence
, 2000
"... Given a propositional theory T and a proposition q, a sufficient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T . In this paper, we propose a notion of strongest necessary and weakest sufficient conditions. ..."
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Cited by 29 (2 self)
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Given a propositional theory T and a proposition q, a sufficient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T . In this paper, we propose a notion of strongest necessary and weakest sufficient conditions. Intuitively, the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory, and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory. We show that these two conditions are dual ones, and can be naturally extended to arbitrary formulas. We investigate some computational properties of these two conditions and discuss some of their potential applications.