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26
Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 538 (13 self)
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Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both prooftheoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...
Applications Of Circumscription To Formalizing Common Sense Knowledge
 Artificial Intelligence
, 1986
"... We present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in (McCarthy 1980) and some applications to formalizing common sense knowledge. The applications in this paper are mostly based on minimizing the abnormality of different aspects o ..."
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Cited by 488 (11 self)
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We present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in (McCarthy 1980) and some applications to formalizing common sense knowledge. The applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities. Included are nonmonotonic treatments of isa hierarchies, the unique names hypothesis, and the frame problem. The new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription. A still more general formalism called prioritized circumscription is briefly explored. 1 INTRODUCTION ANDNEW DEFINITION OF CIRCUMSCRIPTION (McCarthy 1980) introduces the circumscription method of nonmonotonic reasoning and gives motivation, some mathematical properties and some ex1 amples of its application. The present paper is logically selfcontained, but motivation may be enhanced by reading t...
Circumscription
, 1996
"... The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default": ..."
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Cited by 324 (13 self)
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The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default":
On the Declarative and Procedural Semantics of Logic Programs
 Journal of Automated Reasoning
, 1995
"... One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed ..."
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Cited by 65 (8 self)
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One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed to the nonmonotonic character of the negation operator used in logic programs. The problem can therefore be viewed as the problem of finding a suitable formalization of the type of nonmonotonic reasoning used in logic programming. In this paper we introduce a semantics of logic programs based on the class PERF(P) of all, not necessarily Herbrand, perfect models of a program P and we show that the proposed semantics is not only natural but it also combines many of the desirable features of previous approaches, at the same time eliminating some of their drawbacks. For a positive program P, the class PERF(P) of perfect models coincides with the class MIN(P) of all minimal models of P. The per...
Nested Abnormality Theories
 Artificial Intelligence
, 1995
"... We propose a new approach to the use of circumscription for representing knowledge. Nested abnormality theories are similar to simple abnormality theories introduced by McCarthy, except that their axioms may have a nested structure, with each level corresponding to another application of the circ ..."
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Cited by 47 (5 self)
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We propose a new approach to the use of circumscription for representing knowledge. Nested abnormality theories are similar to simple abnormality theories introduced by McCarthy, except that their axioms may have a nested structure, with each level corresponding to another application of the circumscription operator. The new style of applying circumscription sometimes leads to more economical and elegant formalizations. Mathematical properties of nested abnormality theories may be easier to investigate. These advantages are demonstrated by recasting several familiar applications of circumscription in the new format, including some examples of inheritance hierarchies, the domain closure assumption and causal minimization. Nested abnormality theories provide also a convenient representation for the explanation closure approach to the frame problem developed by Schubert.
An Overview of Nonmonotonic Reasoning and Logic Programming
 Journal of Logic Programming, Special Issue
, 1993
"... The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the prehistory of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic ..."
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Cited by 27 (2 self)
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The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the prehistory of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...
A MultiContext Monotonic Axiomatization of Inessential NonMonotonicity
 DIST, University of Genova, Italy
, 1988
"... The main premise of this paper is that certain kinds of nonmonotonic reasoning can be solved within first order logic in a simple monotonic way by formulating problems in a suitable environment. Any problem is formalized as a set of contexts, where a context is a (first order) formalization of a ..."
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Cited by 22 (10 self)
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The main premise of this paper is that certain kinds of nonmonotonic reasoning can be solved within first order logic in a simple monotonic way by formulating problems in a suitable environment. Any problem is formalized as a set of contexts, where a context is a (first order) formalization of a piece of the problem. Reasoning comes out as a result of deduction in different contexts. The claim is that proofs built in this way are clearer and better resemble the kind of explanation that humans give when describing some phenomenon. This thesis is articulated discussing the example about nonmonotonic reasoning reported in [MD80].
Autoepistemic Logics of Closed Beliefs and Logic Programming
 Proceedings of the First International Workshop on Logic Programming and Nonmonotonic Reasoning
, 1995
"... Moore's autoepistemic logic AEL proved to be a very successful approach to formalizing nonmonotonic reasoning and logic programming. However, AEL also has some important drawbacks, e.g., quite "reasonable" theories are often inconsistent in AEL, it does not always lead to the expected, intended s ..."
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Cited by 21 (10 self)
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Moore's autoepistemic logic AEL proved to be a very successful approach to formalizing nonmonotonic reasoning and logic programming. However, AEL also has some important drawbacks, e.g., quite "reasonable" theories are often inconsistent in AEL, it does not always lead to the expected, intended semantics and it cannot be effectively computed even for very simple classes of theories. In this paper we propose a more general approach to autoepistemic reasoning by introducing Autoepistemic Logics of Closed Beliefs AEL cl , where j= cl denotes a specific negative introspection inference operator ("closed world assumption") on which negative introspection in this logic is based. Negative introspection determines which formulae in autoepistemic logic are disbelieved, or, putting it differently, negation of which formulae can be assumed by default. It determines therefore the set of closed world beliefs derivable in a given autoepistemic logic. Moore's autoepistemic logic AEL is a specia...
On the relation between autoepistemic logic and circumscription
 In Proceedings IJCAI89
, 1989
"... Circumscription on the one hand and autoepistemic and default logics on the other seem to have quite different characteristics as formal systems, which makes it difficult to compare them as formalizations of defeasible connmonsense reasoning. In this paper we accomplish two tasks: (1) we extend the ..."
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Cited by 21 (0 self)
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Circumscription on the one hand and autoepistemic and default logics on the other seem to have quite different characteristics as formal systems, which makes it difficult to compare them as formalizations of defeasible connmonsense reasoning. In this paper we accomplish two tasks: (1) we extend the original semantics of autoepistemic logic to a language which includes variables quantified into the context of the autoepistemic operator, and (2) we show that a certain class of autoepistemic theories in the extended language has a minimalmodel semantics corresponding to circumscription. We conclude that all of the firstorder consequences of parallel predicate circumscription can be obtained from this class of autoepistemic theories. The correspondence we construct also sheds light on the problematic treatment of equality in circumscription. 1
An Efficient Method for Eliminating Varying Predicates from a Circumscription
, 1992
"... Circumscription appears to be the most powerful and wellstudied technique used in formalizing commonsense reasoning. The general form of predicate circumscription allows for fixed and varying (floating) predicates. We show that the inference problem under this form of circumscription is efficientl ..."
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Cited by 16 (2 self)
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Circumscription appears to be the most powerful and wellstudied technique used in formalizing commonsense reasoning. The general form of predicate circumscription allows for fixed and varying (floating) predicates. We show that the inference problem under this form of circumscription is efficiently reducible to inferencing under circumscription without varying predicates. In fact, we transform this problem even into circumscription without fixed and varying predicates, that is where all predicates are minimized. Thus any theorem prover or algorithm for inferencing under circumscription without fixed and varying predicates is able to handle inferencing under the general form of predicate circumscription. As a consequence, algorithms that compute circumscription for an inference task can be simplified. Mailing address: Via Salaria 113, I00198 Roma, Italia. Email: cadoli@vaxrma.infn.it y Mailing address: Paniglgasse 16, A1040 Wien, Austria. Internet email: feiter,gottlobg@vexper...