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Uniform Semantic Treatment of Default and Autoepistemic Logics
 ARTIFICIAL INTELLIGENCE
, 2000
"... We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the latti ..."
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Cited by 41 (23 self)
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We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise onetoone correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.
Space Efficiency of Propositional Knowledge Representation Formalisms
 IN PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON THE PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING (KR'96
, 2000
"... We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge #, is the size of the shortest formula of F that represents #. In this paper we assume that knowledge is ..."
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Cited by 26 (3 self)
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We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge #, is the size of the shortest formula of F that represents #. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms ...
Heterogeneous Active Agents
, 1998
"... 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 a ..."
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Cited by 16 (5 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, and study the computation price to be paid (in terms of complexity) for such epistemic desiderata. 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. Last, but not least, we have built a simulation of a Supply Chain application in terms of our theory, building on top of commer...
On the Effect of Default Negation on the Expressiveness of Disjunctive Rules
, 2001
"... In this paper, the expressive power of disjunctive rules involving default negation is analyzed within a framework based on polynomial, faithful and modular (PFM) translations. The analysis is restricted to the stable semantics of disjunctive logic programs. A particular interest is understanding wh ..."
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Cited by 15 (4 self)
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In this paper, the expressive power of disjunctive rules involving default negation is analyzed within a framework based on polynomial, faithful and modular (PFM) translations. The analysis is restricted to the stable semantics of disjunctive logic programs. A particular interest is understanding what is the effect if default negation is allowed in the heads of disjunctive rules. It is established in the paper that occurrences of default negation can be removed from the heads of rules using a PFM translation when default negation is allowed in the bodies of rules. In this case, we may conclude that default negation appearing in the heads of rules does not affect expressive power of rules. However, in the case that default negation may not be used in the bodies of rules, such a PFM translation is no longer possible. Moreover, there is no PFM translation for removing default negation from the bodies of rules. Consequently, disjunctive logic programs with default negation in the bodies of rules are strictly more expressive than those without.
Some (in)translatability results for normal logic programs and propositional theories
 Journal of Applied NonClassical Logics
, 2006
"... ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation f ..."
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Cited by 14 (5 self)
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ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation functions between the classes. As a result, we obtain a strict ordering among the classes under consideration. Binary programs (n ≤ 2) are shown to be as expressive as unconstrained programs but strictly more expressive than unary programs (n ≤ 1) which, in turn, are strictly more expressive than atomic programs (n = 0). We also take propositional theories into consideration and prove them to be strictly less expressive than atomic programs. In spite of the gap in expressiveness, we develop a faithful but nonmodular translation function from normal programs to propositional theories. We consider this as a breakthrough due to subquadratic time complexity (of the order of P   × log 2 Hb(P)). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems.
Fixpoint 3valued semantics for autoepistemic logic
 IN PROCEEDINGS OF THE 15TH NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE. MIT PRESS / AAAIPRESS
, 1998
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On the Intertranslatability of Autoepistemic, Default and Priority Logics, and Parallel Circumscription
 IN PROC. EUROPEAN WORKSHOP ON LOGICS IN ARTIFICIAL INTELLIGENCE (JELIA'98), DAGSTUHL, GERMANY, LNCS 1489
, 1998
"... This paper concentrates on comparing the relative expressive power of five nonmonotonic logics that have appeared in the literature. The results on ..."
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Cited by 11 (1 self)
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This paper concentrates on comparing the relative expressive power of five nonmonotonic logics that have appeared in the literature. The results on
Classifying SemiNormal Default Logic on the Basis of its Expressive Power
 Proceedings of the Fifth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’99), volume 1730 of Lecture Notes in Artificial Intelligence
, 1999
"... This paper reports on systematic research which aims to classify nonmonotonic logics by their expressive power. The classication is based on translation functions that satisfy three important criteria: polynomiality, faithfulness and modularity (PFM for short). The basic method for classication is ..."
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Cited by 10 (3 self)
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This paper reports on systematic research which aims to classify nonmonotonic logics by their expressive power. The classication is based on translation functions that satisfy three important criteria: polynomiality, faithfulness and modularity (PFM for short). The basic method for classication is to prove that PFM translation functions exist (or do not exist) between certain logics. As a result, nonmonotonic logics can be arranged to form a hierarchy. This paper gives an overview of the current expressive power hierarchy (EPH) and investigates seminormal default logic as well as prerequisitefree and seminormal default logic in order to locate their exact positions in the hierarchy. 1
Comparing the Expressive Powers of Some Syntactically Restricted Classes of Logic Programs
 In Proc. 1st International Conference on Computational Logic
, 2000
"... This paper studies the expressive powers of classes of logic programs that are obtained by restricting the number of positive literals (atoms) in the bodies of the rules. Three kinds of restrictions are considered, giving rise to the classes of atomic, unary and binary logic programs. The expres ..."
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Cited by 9 (3 self)
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This paper studies the expressive powers of classes of logic programs that are obtained by restricting the number of positive literals (atoms) in the bodies of the rules. Three kinds of restrictions are considered, giving rise to the classes of atomic, unary and binary logic programs. The expressive powers of these classes of logic programs are compared by analyzing the existence of polynomial, faithful, and modular (PFM) translation functions between the classes. This analysis leads to a strict ordering of the classes of logic programs. The main result is that binary and unary rules are strictly more expressive than unary and atomic rules, respectively. This is the case even if we consider normal logic programs where negative literals may appear in the bodies of rules. Practical implications of the results are discussed in the context of a particular implementation technique for the stable model semantics of normal logic programs, namely contrapositive reasoning with rules. 1