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18
Default Reasoning System DeReS
, 1996
"... In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, finding one or all extensions (if at least one exists) and querying if a formula belongs to one ..."
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Cited by 73 (6 self)
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In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, finding one or all extensions (if at least one exists) and querying if a formula belongs to one or all extensions. If an input theory is a logic program, DeReS computes stable models of this program and supports queries on membership of an atom in some or all stable models. The paper contains an account of our preliminary experiments with DeReS and a discussion of the results. We show that a choice of a propositional prover is critical for the efficiency of DeReS. We also present a general technique that eliminates the need for some global consistency checks and results in substantial speedups. We experimentally demonstrate the potential of the concept of relaxed stratification for making automated reasoning systems practical. 1 INTRODUCTION The area of nonmonotonic l...
Computing With Default Logic
, 1999
"... Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default l ..."
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Cited by 39 (6 self)
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Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of largescale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under i...
Splitting a Default Theory
 In Proc. of AAAI96
, 1996
"... This paper presents mathematical results that can sometimes be used to simplify the task of reasoning about a default theory, by "splitting it into parts." These socalled Splitting Theorems for default logic are related in spirit to "partial evaluation" in logic programming, in ..."
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Cited by 28 (2 self)
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This paper presents mathematical results that can sometimes be used to simplify the task of reasoning about a default theory, by "splitting it into parts." These socalled Splitting Theorems for default logic are related in spirit to "partial evaluation" in logic programming, in which results obtained from one part of a program are used to simplify the remainder of the program. In this paper we focus primarily on the statement and proof of the Splitting Theorems for default logic. We illustrate the usefulness of the results by applying them to an example default theory for commonsense reasoning about action.
Extremal Problems in Logic Programming and Stable Model Computation
"... We study the following problem: given a class of (disjunctive) logic programs C, determine the maximum number of stable models (answer sets) of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of all logic programs of size at mo ..."
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Cited by 10 (1 self)
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We study the following problem: given a class of (disjunctive) logic programs C, determine the maximum number of stable models (answer sets) of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of all logic programs of size at most n. We also characterize the programs for which the maxima are attained. We obtain similar results for the class of all disjunctive logic programs with at most n clauses, each of length at most m, and for the class of all disjunctive logic programs of size at most n. Our results on logic programs have direct implication for the design of algorithms to compute stable models. Several such algorithms, similar in spirit to the DavisPutnam procedure, are described in the paper. 1 Introduction In this paper we study extremal problems appearing in the context of finite propositional logic programs. Specifically, we consider the following problem: given a class of logic programs C, determine th...
A Hierarchy of Tractable Subsets for Computing Stable Models
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1996
"... Finding the stable models of a knowledge base is a significant computational problem in artificial intelligence. This task is at the computational heart of truth maintenance systems, autoepistemic logic, and default logic. Unfortunately, it is NPhard. In this paper we present a hierarchy of clas ..."
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Cited by 5 (0 self)
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Finding the stable models of a knowledge base is a significant computational problem in artificial intelligence. This task is at the computational heart of truth maintenance systems, autoepistemic logic, and default logic. Unfortunately, it is NPhard. In this paper we present a hierarchy of classes of knowledge bases,\Omega 2 ; :::, with the following properties: first,\Omega 1 is the class of all stratified knowledge bases; second, if a knowledge base \Pi is k , then \Pi has at most k stable models, and all of them may be found in time O(lnk), where l is the length of the knowledge base and n the number of atoms in \Pi; third, for an arbitrary knowledge base \Pi, we can find the minimum k such that \Pi belongs in time polynomial in the size of \Pi; and, last, where K is the class of all knowledge bases, it is the case that i=1\Omega i = K, that is, every knowledge base belongs to some class in the hierarchy.
Implementing owl defaults
, 2006
"... Abstract. While it has been argued that knowledge representation for the World Wide Web must respect the open world assumption due to the “open ” nature of the Web, users of the Web Ontology Language (OWL) have often requested some form of nonmonotonic reasoning. In this paper, we present prelimina ..."
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Cited by 4 (1 self)
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Abstract. While it has been argued that knowledge representation for the World Wide Web must respect the open world assumption due to the “open ” nature of the Web, users of the Web Ontology Language (OWL) have often requested some form of nonmonotonic reasoning. In this paper, we present preliminary optimizations and an implementation of a restricted version of Reiter’s default logic as an extension to the description logic fragment of OWL, OWL DL. We implement the decision procedure for this logic in the OWL DL reasoner Pellet, and exploit its support for incremental reasoning through update to improve performance. We also extend an open source ontology editor SWOOP with default rules editing support. 1
An approach to queryanswering in Reiter's default logic and the underlying existence of extensions problem
 Proceedings of the Sixth European Workshop on Logics in Artificial Intelligence
, 1998
"... . We introduce new concepts for default reasoning in the context of queryanswering in regular default logic. For this purpose, we develop a prooforiented approach for deciding whether a default theory has an extension containing a given query. The inherent problem in Reiter's default logic is ..."
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Cited by 2 (1 self)
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. We introduce new concepts for default reasoning in the context of queryanswering in regular default logic. For this purpose, we develop a prooforiented approach for deciding whether a default theory has an extension containing a given query. The inherent problem in Reiter's default logic is that it necessitates the inspection of all default rules for answering no matter what query. Also, default theories are known to lack extensions occasionally. We address these two problems by sloting in a compilation phase before the actual queryanswering phase. The examination of the entire set of default rules is then done only once in the compilation phase; this allows us to inspect only the ultimately necessary default rules during the actual query answering phase. In fact, the latter inspection must not only account for the derivability of the query, but moreover it must guarantee the existence of an encompassing extension. We address this traditionally important problem by furnishing novel...
A Comparison of Two Approaches to Splitting Default Theories
 In AAAI/IAAI
, 1997
"... Default logic is computationally expensive. One of the most promising ways of easing this problem and developing powerful implementations is to split a default theory into smaller parts and compute extensions in a modular, "local" way. This paper compares two recent approaches, Turner&apos ..."
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Cited by 2 (0 self)
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Default logic is computationally expensive. One of the most promising ways of easing this problem and developing powerful implementations is to split a default theory into smaller parts and compute extensions in a modular, "local" way. This paper compares two recent approaches, Turner's splitting and Cholewinski's stratification. It shows that the approaches are closely related  in fact the former can be viewed as a special case of the latter. 1 Introduction Default logic (Reiter 1980) is one of the most prominent approaches of nonmonotonic reasoning, since it provides a formal theory of reasoning based on default rules. One of the main problems with its applicability is that it is computationally harder than classical logic (Marek and Truszczynski 1993, Gottlob 1992), which makes the implementation of powerful systems difficult. A possible solution to this problem might be to split the available knowledge into smaller parts, and to apply default reasoning in a local way. This idea...
Towards Programming in Default Logic
"... In this paper we describe a fragment of default logic suitable for encoding problems from other domains. We investigate a subclass of first order open default theories, which we call extensional default theories. This class of default theories allows easy and compact encodings of problems for expe ..."
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Cited by 1 (0 self)
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In this paper we describe a fragment of default logic suitable for encoding problems from other domains. We investigate a subclass of first order open default theories, which we call extensional default theories. This class of default theories allows easy and compact encodings of problems for experimenting with default reasoning systems. Because most existing systems for default reasoning assume that all input defaults are closed or propositional we show how to transform an extensional default theory to a closed first order default theory or a propositional default theory with same extensions. Finally, we present several encodings of known graph problems in the language of extensional default theories. These encodings can be regarded as benchmark problems for experimenting with nonmonotonic reasoning systems. 1 Introduction In this paper we develop a simple first order nonmonotonic reasoning formalism for describing combinatorial problems Our framework is based on default log...