Hypothesis-based semantics of logic programs in multivalued logics

Loyer, Yann; Spyratos, Nicolas; Stamate, Daniel

doi:10.1145/1013560.1013565

Cited by 16 publications

(21 citation statements)

References 15 publications

(25 reference statements)

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“…Our work generalizes related work such as [2,26,31,32,36]. In [31] it has been shown that the usual semantics of logic programs can be obtained through a unique computation method, but using different uniform assumptions, i.e.…”

Section: Conclusion and Related Workmentioning

confidence: 64%

“…Consider the following case, adapted from [32,36]. A judge is collecting information from two sources, the public prosecutor and the counsel for the defense, in order to decide whether to charge a person named Ted, accused of murder.…”

Section: Mixing Owa and Cwamentioning

confidence: 99%

“…In [2,26] some atoms are allowed to be interpreted according to the OWA, while others are allowed to be interpreted according to the CWA and, thus, roughly the choice of the default is restricted to the value unknown and/or false (additionally, [26] allows to manage default rules as well). Closer to our approach are [32,36]. But, in [36], the extension is confined to particular logic programs for the management of certainty values and limited to the well-founded semantics [50] only and, thus, is just a particular case of our framework.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

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Any-world assumptions in logic programming

Loyer¹,

Straccia²

2005

Theoretical Computer Science

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Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the Closed World Assumption (CWA), which asserts that by default the truth of an atom is false. There is a second well-known assumption, called Open World Assumption (OWA), which asserts that the truth of the atoms is supposed to be unknown by default. However, the CWA, the OWA and the combination of them are extremal, though important, assumptions over a large variety of possible assumptions on the truth of the atoms, whenever the truth is taken from an arbitrary truth space.The topic of this paper is to allow any assignment (i.e. interpretation), over a truth space, to be a default assumption. Our main result is that our extension is conservative in the sense that under the "everywhere false" default assumption (CWA) the usual stable model semantics is captured. Due to the generality and the purely algebraic nature of our approach, it abstracts from the particular formalism of choice and the results may be applied in other contexts as well.

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Section: Conclusion and Related Workmentioning

confidence: 64%

Section: Mixing Owa and Cwamentioning

confidence: 99%

Section: Conclusion and Related Workmentioning

confidence: 99%

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Any-world assumptions in logic programming

Loyer¹,

Straccia²

2005

Theoretical Computer Science

Self Cite

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show abstract

“…In those works, some atoms are allowed to be interpreted according to the OWA, while others are allowed to be interpreted according to the CWA and, thus, roughly the choice of the default is restricted to the value unknown and/or false. The general case, where any assignment may be considered as the default knowledge, is approached in [22], but relying on a weak evaluation of formulas (based on the possible values of unknown atoms), and thus leads to a weaker semantics than the one presented here (that relies on classical formulas evaluation). To the best of our knowledge there is no other work addressing the general case.…”

Section: Introductionmentioning

confidence: 99%

“…To illustrate the idea of non-uniform assumptions, consider the following example. Examples motivating the need for combining OWA and CWA can be found in [10,22,32,33] and in [8].…”

Section: Introductionmentioning

confidence: 99%

Default Knowledge in Logic Programs with Uncertainty

Loyer

Straccia

2003

Logic Programming

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Abstract. Many frameworks have been proposed to manage uncertain information in logic programming. Essentially, they differ in the underlying notion of uncertainty and how these uncertainty values, associated to rules and facts, are managed. The goal of this paper is to allow the reasoning with non-uniform default assumptions, i.e. with any arbitrary assignment of default values to the atoms. Informally, rather than to rely on the same default certainty value for all atoms, we allow arbitrary assignments to complete information. To this end, we define both epistemologically and computationally the semantics according to any given assumption. For reasons of generality, we present our work in the framework presented in [17] as a unifying umbrella for many of the proposed approaches to the management of uncertainty in logic programming. Our extension is conservative in the following sense: (i) if we restrict our attention to the usual uniform Open World Assumption, then the semantics reduces to the Kripke-Kleene semantics, and (ii) if we restrict our attention to the uniform Closed World Assumption, then our semantics reduces to the well-founded semantics.

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4-Valued Semantics Under the OWA: A Deductive Database Approach

Laurent¹

2020

Communications in Computer and Information Science

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In this paper, we introduce a novel approach for dealing with databases containing inconsistent information. Considering four-valued logics in the context of OWA (Open World Assumption), a database ∆ is a pair (E, R) where E is the extension and R the set of rules. In our formalism, the set E is a set of pairs of the form ϕ, v where ϕ is a fact and v is either t, or b, or f (meaning respectively true, inconsistent or false), given that unknown facts are not stored. Moreover the rules extend Datalog neg rules allowing their heads to be a negative atom. We then define the notion of model of such a database, we show how to compute one particular model called semantics, and we investigate properties of this model. We also show how our approach applies to data integration and we review examples from the literature.

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Hypothesis-based semantics of logic programs in multivalued logics

Cited by 16 publications

References 15 publications

Any-world assumptions in logic programming

Any-world assumptions in logic programming

Default Knowledge in Logic Programs with Uncertainty

4-Valued Semantics Under the OWA: A Deductive Database Approach

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