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17
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...
Reasoning with Stratified Default Theories
, 1995
"... Default logic is one of the principal formalisms for nonmonotonic reasoning. In this paper, we study algorithms for computing extensions for a class of general propositional default theories. We focus on the problem of partitioning a given set of defaults into a family of its subsets. Then we in ..."
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Cited by 17 (3 self)
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Default logic is one of the principal formalisms for nonmonotonic reasoning. In this paper, we study algorithms for computing extensions for a class of general propositional default theories. We focus on the problem of partitioning a given set of defaults into a family of its subsets. Then we investigate how the results obtained for these subsets can be put together to achieve the extensions of the original theory. The method we propose is designed to prune the search space and reduce the number of calls to propositional provability procedure. It also constitutes a simple and uniform framework for the design of parallel algorithms for computing extensions.
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.
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...
Locally determined logic programs and recursive stable models
 Annals of Mathematics and Arti Intelligence
"... Abstract. In general, the set of stable models of a recursive logic program can be quite complex. For example, it follows from results of Marek, Nerode, and Remme [17] that there exists finite predicate logic programs and recursive propositional logic programs which have stable models but no hyperar ..."
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Cited by 1 (1 self)
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Abstract. In general, the set of stable models of a recursive logic program can be quite complex. For example, it follows from results of Marek, Nerode, and Remme [17] that there exists finite predicate logic programs and recursive propositional logic programs which have stable models but no hyperarithmetic stable models. In this paper, we shall define several conditions which ensure that a recursive propositional logic program P has a stable model which is of low complexity, that is, a recursive stable model, a polynomial time stable model, or a stable model which lies in a low level of the polynomial time hierarchy.
Compactness properties for stable semantics of logic programs
, 2006
"... Logic programming with stable logic semantics (SLP) is a logical formalism that assigns to sets of clauses in the language admitting negations in the bodies a special kind of models, called stable models. This formalism does not have the compactness property. We show a number of conditions that enta ..."
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Logic programming with stable logic semantics (SLP) is a logical formalism that assigns to sets of clauses in the language admitting negations in the bodies a special kind of models, called stable models. This formalism does not have the compactness property. We show a number of conditions that entail a form of compactness for SLP. 1
Learning Mechanism for Distributed Default Logic Based MAS – Implementation Considerations ∗
"... The paper presents learning mechanisms for MAS based on Distributed Default Logic (DDL), the formalism for multiagent knowledge representation and reasoning. In the distributed environment learning processes provide measures to order default rules, which gives the agent better use of its local and ..."
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The paper presents learning mechanisms for MAS based on Distributed Default Logic (DDL), the formalism for multiagent knowledge representation and reasoning. In the distributed environment learning processes provide measures to order default rules, which gives the agent better use of its local and external knowledge. Such mechanisms allow the system to work effectively in a changing environment, where basic facts and sources of information are uncertain.
Computing Default Logic Extensions: An lementation
"... Default logic [3] is a useful formalism for reasoning with incomplete information, its intuitive characteristics making it particularly suited for applications. Exten is a system currently capable of computing firstorder Reiter, Justified and Constrained default extensions. It is part of a project t ..."
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Default logic [3] is a useful formalism for reasoning with incomplete information, its intuitive characteristics making it particularly suited for applications. Exten is a system currently capable of computing firstorder Reiter, Justified and Constrained default extensions. It is part of a project to create a full default logic workbench, with future work involving query evaluation, further support for default variants and integration with belief revision. As such, it has been implemented in an objectoriented manner, and is designed to facilitate experimentation. The interface is based around a small language, giving the user flexibility in editing default theories and changing various parameters (such as compute next n extensions or carry out ‘success ’ checks every m steps). Default reasoning is known to be computationally hard. One efficiency increasing technique used in Exten is stratification [l] which, if applicable, allows the computation of extensions in a modular way. Exten uses a forwardchaining approach and applies additional pruning techniques, some of which are outlined below.