Partial evidential stable models for disjunctive deductive databases

Seipel, Dietmar

doi:10.1007/bfb0054790

Cited by 14 publications

(11 citation statements)

References 14 publications

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“…Notably, it appeared that semi-equilibrium models coincide with evidential stable models in [51]; our semantic and computational results thus carry over to them. Different from other formalisms such as CR-Prolog [4] or generalized stable models [30], unsupported assumptions in semi-stable and semi-equilibrium models serve to block rules but not to establish positive evidence for deriving atoms from rules.…”

Section: Resultssupporting

confidence: 63%

“…Motivated by the fact that a disjunctive deductive database (DDDB) may lack stable models or even P-stable models, Seipel [51] presented a paracoherent semantics, called the evidential stable model (ESM) semantics, which assigns some model to every DDDB (that is, to every constraint-free disjunctive logic program), such that the properties (D1)-(D3) in the Introduction are satisfied. Similar to [49], but guided by slightly different intuition, he defined the evidential stable models of a program P in a two-step process.…”

Section: Evidential Stable Modelsmentioning

confidence: 99%

“…[4,19,39,43,44,47,48,51,56,59]. Ideally, such a relaxation meets for a program P the following properties:…”

Section: Introductionmentioning

confidence: 99%

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Semi-equilibrium models for paracoherent answer set programs

Amendola

Eiter

Fink

et al. 2016

Artificial Intelligence

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The answer set semantics may assign a logic program to model, due to logical contradiction or unstable negation, which is caused by cyclic dependency of an atom on its negation. While logical contradictions can be handled with traditional techniques from paraconsistent reasoning, instability requires other methods. We consider resorting to a paracoherent semantics, in which 3-valued interpretations are used where a third truth value besides true and false expresses that an atom is believed true. This is at the basis of the semi-stable model semantics, which was defined using a program transformation. In this paper, we give a model-theoretic characterization of semi-stable models, which makes the semantics more accessible. Motivated by some anomalies of semi-stable model semantics with respect to basic epistemic properties, we propose an amendment that satisfies these properties. The latter has both a transformational and a model-theoretic characterization that reveals it as a relaxation of equilibrium logic, the logical reconstruction of answer set semantics, and is thus called the semi-equilibrium model semantics. We consider refinements of this semantics to respect modularity in the rules, based on splitting sets, the major tool for modularity in modeling and evaluating answer set programs. In that, we single out classes of canonical models that are amenable for customary bottom-up evaluation of answer set programs, with an option to switch to a paracoherent mode when lack of an answer set is detected. A complexity analysis of major reasoning tasks shows that semi-equilibrium models are harder than answer sets (i.e., equilibrium models), due to a global minimization step for keeping the gap between true and believed true atoms as small as possible. Our results contribute to the logical foundations of paracoherent answer set programming, which gains increasing importance in inconsistency management, and at the same time provide a basis for algorithm development and integration into answer set solvers.

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Section: Resultssupporting

confidence: 63%

Section: Evidential Stable Modelsmentioning

confidence: 99%

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Semi-equilibrium models for paracoherent answer set programs

Amendola

Eiter

Fink

et al. 2016

Artificial Intelligence

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“…The two major paracoherent semantics for logic programs are the semi-stable (Sakama and Inoue 1995) and the semi-equilibrium semantics (Amendola et al 2016). These semantics emerged over several alternative proposals (Przymusinski 1991a;Gelder et al 1991;Saccà and Zaniolo 1991;You and Yuan 1994;Eiter et al 1997;Seipel 1997;Balduccini and Gelfond 2003;Pereira and Pinto 2005;Pereira and Pinto 2007;Alcântara et al 2005;Galindo et al 2008). However, (Amendola et al 2016) have shown that only semi-stable semantics (Sakama and Inoue 1995) and semi-equilibrium semantics (Amendola et al 2016) satisfy all the following five highly desirable -from the knowledge representation point of viewtheoretical properties: (i) every consistent answer set of a program corresponds to a paracoherent answer set (answer set coverage); (ii) if a program has some (consistent) answer set, then its paracoherent answer sets correspond to answer sets (congruence); (iii) if a program has a classical model, then it has a paracoherent answer set (classical coherence); (iv) a minimal set of atoms should be undefined (minimal undefinedness); (v) every true atom must be derived from the program (justifiability or foundedness).…”

Section: Paracoherent Semanticsmentioning

confidence: 99%

Paracoherent Answer Set Semantics meets Argumentation Frameworks

Amendola

Ricca

2019

Theory and Practice of Logic Programming

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In the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the wellknown stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained. Under consideration for acceptance in TPLP.

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“…The literature on inconsistency in deductive databases and logic programs is large [10] but I think that there is little references on abstract negation.…”

Section: Examplesmentioning

confidence: 99%