Partial equilibrium logic

Cabalar, Pedro; Odintsov, Sergei P.; Pearce, David; Valverde, Agustín

doi:10.1007/s10472-007-9075-0

Cited by 12 publications

(11 citation statements)

References 36 publications

(46 reference statements)

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“…(1) One way is to exclude constraints (or less restrictive, cross-constraints), and resort instead to the usage of rules which create unstable negation; that is ← Body (13) is replaced with f ← Body, not f , (14) where f is a fresh atom. Indeed, on some (early) implementations of answer set solvers constraints have been provided in this way.…”

Section: Mj C-split Sequences and Modelsmentioning

confidence: 99%

“…Indeed, on some (early) implementations of answer set solvers constraints have been provided in this way. The SEQ-model semantics is able to distinguish between (13) and (14); this can be exploited to use (14) as a soft constraint that may intuitively be violated if needed to achieve an EQ-model resp. answer set; indeed, this rule can always be satisfied by considering f as believed true.…”

Section: Mj C-split Sequences and Modelsmentioning

confidence: 99%

“…We then have WF(P ) = (I, J ) where I is the least fixpoint of the monotonic operator γ 2 P (X) = γ P (γ P (X)), and J = γ P (I). Furthermore, the well-founded model is the least partial stable model (see Section 8.2.4 below); it has been characterized in the logic HT 2 in terms of the partial equilibrium model that leaves the most atoms undefined [14].…”

Section: Well-founded Semanticsmentioning

confidence: 99%

“…Like the well-founded model, P-stable models can be characterized in several ways (cf. [19]); with respect to equilibrium logic, Cabalar et al [14] semantically characterized P-stable models in the logic HT 2 in terms of partial equilibrium models. For the concerns of our discussion, we use here a characterization of P-stable models (X, Y ) in terms of the multi-valued operator γ P (X) = MM(P X ) as the HT-interpretations (X, Y ) such that Y ∈γ P (X) and X ∈γ P (Y ); this characterization is easily obtained from [19].…”

Section: Partial Stable Model Semanticsmentioning

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: Mj C-split Sequences and Modelsmentioning

confidence: 99%

Section: Mj C-split Sequences and Modelsmentioning

confidence: 99%

Section: Well-founded Semanticsmentioning

confidence: 99%

Section: Partial Stable Model Semanticsmentioning

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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“…Additionally, there have been defined some specialized RIF Dialects to cover the syntax of semantics of disjunctive logic programs under the stable model semantics RIF-CASPD ( [24]) and well-founded semantics with default and strong (symmetric) negation RIF-CLPWD ( [25]). However, the approach followed in the definitions of RIF-CASPD and RIF-CLPWD is against the current trends in the literature for defining the semantics of logic programs [22,10,9] because of the way RIF-FLD semantics has been defined. Namely, RIF-CASPD and RIF-CLPWD resort to an explicit quotient syntactic definition in order to obtain the intended models, while in the approaches of [22,10,9] this is fully captured model-theoretically by appropriate definitions of the truth-value lattices and interpretation of logical connectives.…”

Section: Basics Of Rule Interchange Format Semanticsmentioning

confidence: 99%

Modularity in the Rule Interchange Format

Damásio

Analyti

Antoniou

2011

Rule-Based Reasoning, Programming, and Applications

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Abstract. The adoption of standards by the knowledge representation and logic programming communities is essential for their visibility and impact. The Rule Interchange Format is a fundamental effort in this direction that should be supported by users, developers and theoreticians. For this reason, it is essential to the community to discuss the recommendations published by the W3C RIF Working Group. In particular, this paper presents the semantics of Rule Interchange Format (RIF) of multidocuments, analyses it and some deficiencies are elicited. A more general approach is proposed as an alternative semantics for multi-documents. As a side important result, some relevant problems in the semantics of RIF-FLD are also discussed and possible ways out are proposed.

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A Sequent-Type Calculus for Three-Valued Default Logic, Or: Tweety Meets Quartum Non Datur

Pkhakadze

Tompits

2019

Logic Programming and Nonmonotonic Reasoning

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Partial equilibrium logic

Cited by 12 publications

References 36 publications

Semi-equilibrium models for paracoherent answer set programs

Semi-equilibrium models for paracoherent answer set programs

Modularity in the Rule Interchange Format

A Sequent-Type Calculus for Three-Valued Default Logic, Or: Tweety Meets Quartum Non Datur

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