Proceedings Article•
Logic programs with classical negation
01 May 1990-pp 579-597
About: This article is published in International Conference on Lightning Protection.The article was published on 1990-05-01 and is currently open access. It has received 602 citations till now. The article focuses on the topics: Negation & Predicate functor logic.
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TL;DR: It is shown that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available.
Abstract: An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.
2,451 citations
Cites background from "Logic programs with classical negat..."
...(Section 2), this rule is obtained from a rule ( 7 ) of II by deleting not Lm+l ........
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...( i ) for any ground instance ( 7 ) of any default from D, if G ~ FD(E) and //1 ........
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...*** In the notation of Ref. 25), ( 7 ) would be written as...
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TL;DR: It is shown that the novel paradigm embeds classical logical satisfiability and standard (finite domain) constraint satisfaction problems but seems to provide a more expressive framework from a knowledge representation point of view.
Abstract: Logic programming with the stable model semantics is put forward as a novel constraint programming paradigm. This paradigm is interesting because it bring advantages of logic programming based knowledge representation techniques to constraint programming and because implementation methods for the stable model semantics for ground (variabledfree) programs have advanced significantly in recent years. For a program with variables these methods need a grounding procedure for generating a variabledfree program. As a practical approach to handling the grounding problem a subclass of logic programs, domain restricted programs, is proposed. This subclass enables efficient grounding procedures and serves as a basis for integrating builtdin predicates and functions often needed in applications. It is shown that the novel paradigm embeds classical logical satisfiability and standard (finite domain) constraint satisfaction problems but seems to provide a more expressive framework from a knowledge representation point of view. The first steps towards a programming methodology for the new paradigm are taken by presenting solutions to standard constraint satisfaction problems, combinatorial graph problems and planning problems. An efficient implementation of the paradigm based on domain restricted programs has been developed. This is an extension of a previous implementation of the stable model semantics, the Smodels system, and is publicly available. It contains, e.g., builtdin integer arithmetic integrated to stable model computation. The implementation is described briefly and some test results illustrating the current level of performance are reported.
967 citations
Cites background from "Logic programs with classical negat..."
...Furthermore, logic program rules can be seen as default rules in Reiter’s default logic [31] and then stable models correspond to default extensions [18]....
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TL;DR: The work reported here introducesdefeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation and a defeasible argumentation inference mechanism for warranting the entailed conclusions.
Abstract: The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query $q$ will succeed when there is an argument ${\mathcal A}$ for $q$ that is warranted, i.e. the argument ${\mathcal A}$ that supports $q$ is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.
878 citations
Cites background or methods from "Logic programs with classical negat..."
...Strong negation was introduced in Extended Logic Programming (Gelfond & Lifschitz, 1990)....
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...The change reflects that when an extended literal is found in the body of a rule, that literal will be ignored: 4 Adapted from an example attributed to John McCarthy in (Gelfond & Lifschitz, 1990)....
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...If a contradictory set Π is used in a de.l.p. then the answer would be Lit , as in Extended Logic Programming....
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...In (Gelfond & Lifschitz, 1990), Logic Programming with Classical Negation was introduced....
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...This problem was attacked in (Inoue, 1991), where Extended Logic Programming with Default Assumptions is considered....
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TL;DR: An abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases, is presented and a more liberal, argumentation-theoretic semantics is proposed, based upon the notion of admissible extension in logic programming.
687 citations
TL;DR: The evolution of argumentation is traced from the mid-1980s to the present, as argument in embedded in different complex systems for real-world applications, and allow more formal work to be done in different areas, such as AI and Law, case-based reasoning and negotiation among intelligent agents.
Abstract: Logical models of arguement formalize commonsense reasoning while taking process and computation seriously. This survey discusses the main ideas that characterize different logical models of argument. It presents the formal features of a few features of a few main approaches to the modeling of argumentation. We trace the evolution of argumentation from the mid-1980s, when argument systems emerged as an alternative to nonmonotonic formalisms based on classical logic, to the present, as argument in embedded in different complex systems for real-world applications, and allow more formal work to be done in different areas, such as AI and Law, case-based reasoning and negotiation among intelligent agents.
565 citations