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Smallest Equivalent Sets for Finite Propositional Formula Circumscription
, 2000
"... Abstract Circumscription uses classical logic in order to modelize rules with exceptions and implicit knowledge. Formula circumscription is known to be easier to use in order to modelize a situation. We describe when two sets of formulas give the same result, when circumscribed. Two kinds of such eq ..."
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Cited by 1 (1 self)
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Abstract Circumscription uses classical logic in order to modelize rules with exceptions and implicit knowledge. Formula circumscription is known to be easier to use in order to modelize a situation. We describe when two sets of formulas give the same result, when circumscribed. Two kinds
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 532 (12 self)
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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
History of circumscription
 Artificial Intelligence
, 1993
"... 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 va ..."
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Cited by 10 (0 self)
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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
Loop formulas for circumscription
 Artificial Intelligence
, 2004
"... Clark’s completion is a simple nonmonotonic formalism and a special case of many nonmonotonic logics. Recently there has been work on extending completion with “loop formulas ” so that general cases of nonmonotonic logics such as logic programs (under the answer set semantics) and McCain–Turner caus ..."
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Cited by 25 (15 self)
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Cain–Turner causal logic can be characterized by propositional logic in the form of “completion + loop formulas”. In this paper, we show that the idea is applicable to McCarthy’s circumscription in the propositional case. We also show how to embed propositional circumscription in logic programs and in causal logic
The Complexity of Model Checking for Circumscriptive Formulae
 Information Processing Letters
, 1992
"... this paper we carry out a detailed analysis of the computational complexity of model checking for propositional circumscriptive formulae. Following Schaefer's approach [6], we classify propositional formulae according to the logical relations which are used to represent them. Using the results ..."
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Cited by 54 (5 self)
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this paper we carry out a detailed analysis of the computational complexity of model checking for propositional circumscriptive formulae. Following Schaefer's approach [6], we classify propositional formulae according to the logical relations which are used to represent them. Using
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"... Generalized vs formula circumscription over finite models (extended abstract) ..."
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Generalized vs formula circumscription over finite models (extended abstract)
Inverse Circumscription
"... Inverse (or identification) problems involve deciding whether or not an explicitly given set of data points have an implicit description, for instance, in the form of a constraint network. Such problems provide insight into the relationships among various representations of knowledge, which may ..."
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may have differing computational properties. This paper formalizes and studies the inverse circumscription problem, which (roughly speaking) is to decide, given a set of models, if there exists a formula whose circumscription describes the input set.
Computing Protected Circumscription
, 1985
"... : This paper deals with computing circumscription in the case of Horn data with addi ional protection (indefinite data), an intermediate investigation between Reiter's result on predicate a c completion and Lifschitz's efforts to make general (formula) circumscription more efficient as omp ..."
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Cited by 13 (3 self)
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: This paper deals with computing circumscription in the case of Horn data with addi ional protection (indefinite data), an intermediate investigation between Reiter's result on predicate a c completion and Lifschitz's efforts to make general (formula) circumscription more efficient
Stable Models and Circumscription
, 2007
"... The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (includ ..."
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Cited by 71 (37 self)
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(including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of secondorder logic that is similar to the formula familiar
Eliminating the fixed predicates from a circumscription
 Artificial Intelligence
, 1989
"... Parallel predicate circumscription is the primary circumscriptive technique used in formalizing commonsense reasoning. In this paper we present a direct syntactic construction for transforming any parallel predicate circumscription usingfixed predicates into an equivalent one which does not. Thus, w ..."
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Cited by 31 (0 self)
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and assumptionbased truth maintenance) and for implementing fixed predicates. Circumscription is one of the most welldeveloped formalizations of nonmonotonic reasoning. It exists in many variants, including domain cirdumscription [10], predicate circumscription [9], parallel predicate circumscription [9], formula
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