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Logic Programming and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
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Cited by 273 (8 self)
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We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
A Classification Theory of Semantics of Normal Logic Programs: II. Weak Properties
 FUNDAMENTA INFORMATICAE
, 1995
"... Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a ..."
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Cited by 81 (0 self)
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Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a sceptical nonmonotonic entailment relation SEM scept . We ask for the properties of these sceptical relations and use them to describe all possible semantics. We collect in this paper serious shortcomings of some semantics proposed recently. Their strange behaviour led us to formulate in a natural way certain principles to avoid these problems. We argue that any wellbehaved semantics should satisfy these principles. The main results state that our list of weak principles is complete in the following sense: any wellbehavedsemantics is an extension of the wellfounded semantics WFS and coincides for stratified programs with Apt, Blair, and Walker's supported model M supp P . We also...
Scenario Semantics of Extended Logic Programs
, 1993
"... We present a coherent, flexible, unifying, and intuitive framework for the study of explicit negation in logic programs, based on the notion of admissible scenaria and the "coherence principle". With this support we introduce, in a simple way, a proposed "ideal sceptical semantics&quo ..."
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Cited by 17 (6 self)
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We present a coherent, flexible, unifying, and intuitive framework for the study of explicit negation in logic programs, based on the notion of admissible scenaria and the "coherence principle". With this support we introduce, in a simple way, a proposed "ideal sceptical semantics", as well as its well founded counterpart. Another result is a less sceptical "complete scenaria semantics", and its proof of equivalence to the wellfounded semantics with explicit negation (WFSX). This has the added benefict of bridging complete scenaria to default theory via WFSX, defined here based on GelfondLifschitz \Gamma operator.. Finally, we characterize a variety of more and less sceptical or credulous semantics, including answersets, and give sufficient conditions for equivalence between those semantics. Introduction In general, approaches to semantics follow two major intuitions: scepticism and credulity [30]. In logic programming, the credulous approach includes such semantics as stabl...
Layered models topdown querying of normal logic programs
 IN TO APPEAR IN PROCEEDINGS OF THE PRACTICAL ASPECTS OF DECLARATIVE LANGUAGES, LNCS
, 2009
"... For practical applications, the use of topdown querydriven proofprocedures is essential for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a topdown search method. A querysolving engine is thus hi ..."
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For practical applications, the use of topdown querydriven proofprocedures is essential for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a topdown search method. A querysolving engine is thus highly desirable. The current standard 2valued semantics for Normal Logic Programs (NLPs), the Stable Models (SMs) semantics, does not allow for topdown querysolving because it does not enjoy the relevance property — and moreover, it does not guarantee the existence of a model for every NLP. To overcome these current limitations we introduce here a new 2valued semantics for NLPs — the Layered Models semantics — which conservatively extends the SMs, enjoys relevance and guarantees model existence among other useful properties. Moreover, for existential query answering there is no need to compute total models, but just the partial models that sustain the answer to the query, or one might simply know a model one exists without producing it; relevance ensures these can be extended to total models. A first implementation of a querysolving engine based on this new semantics is presented and described here. It uses the XSBProlog engine and its XASP interface to Smodels, thereby providing a useful tool built as a hybrid of the two systems and taking advantage of the best of each. Conclusions and further work end the paper.
An Abductive Approach to Disjunctive Logic Programming
 JOURNAL OF LOGIC PROGRAMMING
, 2000
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Regular Extension Semantics and Disjunctive EshghiKowalski Procedure
 IN PROC. JICSLP '98
, 1998
"... Can the elegant abductive proof procedure by Eshghi and Kowalski be extended to answer queries for disjunctive logic programs? If yes, what is the semantics that such an extended procedure computes? Several years ago, in an unpublished manuscript Dung specified a proof procedure that embeds a form o ..."
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Cited by 3 (1 self)
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Can the elegant abductive proof procedure by Eshghi and Kowalski be extended to answer queries for disjunctive logic programs? If yes, what is the semantics that such an extended procedure computes? Several years ago, in an unpublished manuscript Dung specified a proof procedure that embeds a form of linear resolution into the EshghiKowalski procedure [3]. More recently, You et al. defined the regular extension semantics for disjunctive programs [19], which was strongly motivated by the observation that some forms of extended EshghiKowalski procedure could be used to answer queries under this semantics. This paper reports the finding that a variant of the procedure specified by Dung computes the regular extension semantics.
Stable versus layered logic program semantics
, 2009
"... For practical applications, the use of topdown querydriven proofprocedures is convenient for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a topdown search method. A 2valued semantics for Normal L ..."
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For practical applications, the use of topdown querydriven proofprocedures is convenient for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a topdown search method. A 2valued semantics for Normal Logic Programs (NLPs) allowing for topdown querysolving is thus highly desirable, but the Stable Models semantics (SM) does not allow it, for lack of the relevance property. To overcome this limitation we introduced in [24], and review here, a new 2valued semantics for NLPs — the Layer Supported Models semantics — which conservatively extends the SM semantics, enjoys relevance and cumulativity, guarantees model existence, and respects the WellFounded Model. In this paper we also exhibit a transformation, TR, from one propositional NLP into another, whose Layer Supported Models are precisely the Stable Models of the transform, which can then be computed by extant Stable Model implementations, providing a tool for the immediate generalized use of the new semantics and its applications. In the context of abduction in Logic Programs, when finding an abductive solution for a query, one may want to check too whether some other literals become true (or false) as a consequence, strictly within the abductive solution found, that is without performing additional abductions, and without having to produce a complete model to do so. That is, such consequence literals may consume, but not produce, the abduced literals of the solution. To accomplish this mechanism, we present the concept of Inspection Point in Abductive Logic Programs, and show, by means of examples, how one can employ it to investigate sideeffects of interest (the inspection points) in order to help choose among abductive solutions.
Cautious Models for General Logic Programs
 IN PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON DEDUCTIVE DATABASES AND LOGIC PROGRAMMING
, 1995
"... In this paper, cautious models of general logic programs are investigated. Such models are constructed iteratively using a monotonic operator which performs case analysis on total interpretations generated by enumerations of atoms. Consequently, every general logic program has a unique cautious mode ..."
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Cited by 2 (2 self)
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In this paper, cautious models of general logic programs are investigated. Such models are constructed iteratively using a monotonic operator which performs case analysis on total interpretations generated by enumerations of atoms. Consequently, every general logic program has a unique cautious model. The new class of partial models is compared with wellfounded and stable models of general logic programs. Various extensions of these models are are also addressed. The time complexity of constructing cautious models is analyzed. Results indicate that the major reasoning task is coNPcomplete. Finally, the connection to cautious autoepistemic logic is explained.
An Argumentation Theoretic Semantics Based on NonRefutable Falsity
"... Introduction In [PAA TCS] we've argued before that the WFS of normal programs is too sceptical, and then defined the more credulous Osemantics for normal programs. Take: arrested not free free not free free not arrested . In the WFM, argument not arrested is not acceptable because ..."
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Introduction In [PAA TCS] we've argued before that the WFS of normal programs is too sceptical, and then defined the more credulous Osemantics for normal programs. Take: arrested not free free not free free not arrested . In the WFM, argument not arrested is not acceptable because free} is evidence against it. So WFM = {}. . However free} is inconsistent, and should not count as evidence. . not arrested can be safely assumed: the only way to support arrested is inconsistent. The Osemantics is {free, not arrested}. Principles of Osemantics Any MOD(P ) can be added with a set A of negative literals (assumptions) if the following principles hold: . Consistent: MOD(P )#A #= L for not L A. . Sustainable: for not L A there is no consistent set A of assumptions defeating not L, i.e. such that MOD(P ) = . Maximal . Unique: There is consensus about a unique such set A. Introduction (cont.) We've defined WFSX [PA ECAI], extending WFS with
Tight Semantics for Logic Programs
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
"... We define the Tight Semantics (TS), a new semantics for all NLPs complying with the requirements of: 2valued semantics; preserving the models of SM; guarantee of model existence (even in face of odd loops over negation or infinite chains); relevance; cumulativity; and compliance with the WellFound ..."
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We define the Tight Semantics (TS), a new semantics for all NLPs complying with the requirements of: 2valued semantics; preserving the models of SM; guarantee of model existence (even in face of odd loops over negation or infinite chains); relevance; cumulativity; and compliance with the WellFounded Model. We also extend TS to adumbrate ELPs and Disjunctive LPs, though a full account of these is left to other papers. When complete models are unnecessary, and topdown querying (à la Prolog) is desired, TS provides the 2valued option that guarantees model existence, as a result of its relevance property. Topdown querying with abduction by need is rendered available too by TS. The user need not pay the price of computing whole models, nor of generation all possible abductions, only to filter irrelevant ones subsequently. In a nutshell, a TS model of a NLP P is any minimal model M of P that further satisfies bP —the program remainder of P —in that each loop in b P has a minimal model contained in M, whilst respecting the constraints imposed by the minimal models of the other loops soconstrained too. The applications afforded by TS are all those of Stable Models, which it generalizes, plus those permitting to solve OLONs for model existence, plus those employing OLONs for productively obtaining problem solutions, not just filtering them (like ICs).