A Crash Course on Generalized Possibilistic Logic

Dubois, Didier; Prade, Henri

doi:10.1007/978-3-030-00461-3_1

Cited by 8 publications

(5 citation statements)

References 27 publications

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“…Possibilistic logic and possibility theory [3,25,28] are important frameworks for reasoning under uncertainty. Uncertain information can either be represented in extension by means of the so-called possibility distributions, or in a compact way by means of the so-called weighted logics or graphical models.…”

Section: Possibilistic Dl-lite Knowledge Basementioning

confidence: 99%

Computing a Possibility Theory Repair for Partially Preordered Inconsistent Ontologies

Belabbès¹,

Benferhat

2022

IEEE Trans. Fuzzy Syst.

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We address the problem of handling inconsistency in uncertain knowledge bases that are specified in the lightweight fragments of Description Logics DL-Lite. More specifically, we assume that the TBox component is coherent, stable and fully reliable. However, the ABox component may be inconsistent with respect to the TBox, partially preordered and uncertain. Uncertainty is encoded in the framework of possibility theory. In this context, we propose an extension of standard possibilistic DL-Lite. We represent the ABox as a symbolic weighted base, where the weights attached to the assertions are ordered according to a strict partial order. We define a tractable method for computing a single possibilistic repair for a partially preordered weighted ABox. The idea is to consider the possibilistic compatible bases of such an ABox, which intuitively encode all the possible extensions of a partial order, and compute the possibilistic repair of each compatible base. We then compute the intersection of all these possibilistic repairs to obtain a single repair for the initial ABox. We also provide an equivalent characterization by introducing the notion of π-accepted assertions. This ensures that the computation of the partially preordered possibilistic repair can be achieved in polynomial time in DL-Lite.

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Section: Possibilistic Dl-lite Knowledge Basementioning

confidence: 99%

Computing a Possibility Theory Repair for Partially Preordered Inconsistent Ontologies

Belabbès¹,

Benferhat

2022

IEEE Trans. Fuzzy Syst.

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“…Possibilistic logic (PL) [31,39,41,42] amounts to a classical logic handling of certaintyqualified statements. Certainty is estimated in the setting of possibility theory as a lower bound of a necessity set-function.…”

Section: Possibilistic Logic and Its Applicationsmentioning

confidence: 99%

“…GPL can be viewed as both a generalization of PL and a generalization of Meta-Epistemic Logic (MEL) [3], the simplest logic of belief and partial ignorance -a fragment of modal logic KD where all formulas are modal, and modalities cannot be nested. See Figure 1 [41], which points out how GPL extends propositional logic through MEL and PL. GPL is in fact just a two-tiered standard propositional logic, in which propositional formulas are encapsulated by weighted modal operators, forming higher order propositional formulas, interpreted in terms of uncertainty measures from possibility theory.…”

Section: Generalized Possibilistic Logicmentioning

confidence: 99%

Possibility Theory and Possibilistic Logic: Tools for Reasoning Under and About Incomplete Information

Dubois

Prade

2021

IFIP Advances in Information and Communication Technology

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“…A restriction in standard possibilistic logic is that only conjunctions of weighted formulas are allowed. Dubois et al [28,29,27] have conceived the Generalized Possibilistic Logic (GPL) in which the disjunction and the negation of standard possibilistic formulas are handled. In this logic, for instance the formula (∨ ϕ : α ψ : β ) belongs to the GPL's language, and since possibility-valued formulas are also smoothly embedded in GPL, formulas like the next one belong to GPL: {∧ (∨ P Q) : N 1 ¬Q : N .75 ¬ (∨ ¬P R) : N 1 (∨ ¬R : Π .75 ϕ : Π .25 ) } One can see that in GPL, connectives can be internal or external (GPL is a two-tired logic) with their corresponding and different semantics, and also, GPL formulas can be expressed in NC form.…”

Section: Generalized Possibilistic Logicmentioning

confidence: 99%

The Possibilistic Horn Non-Clausal Knowledge Bases

Imaz¹

2021

Preprint

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Posibilistic logic is the most extended approach to handle uncertain and partially inconsistent information. Regarding normal forms, advances in possibilistic reasoning are mostly focused on clausal form. Yet, the encoding of real-world problems usually results in a non-clausal (NC) formula and NC-to-clausal translators produce severe drawbacks that heavily limit the practical performance of clausal reasoning. Thus, by computing formulas in its original NC form, we propose several contributions showing that notable advances are also possible in possibilistic non-clausal reasoning.Firstly, we define the class of Possibilistic Horn Non-Clausal Knowledge Bases, or H Σ , which subsumes the classes: possibilistic Horn and propositional Horn-NC. H Σ is shown to be a kind of NC analogous of the standard Horn class.Secondly, we define Possibilistic Non-Clausal Unit-Resolution, or UR Σ , and prove that UR Σ correctly computes the inconsistency degree of H Σ members. UR Σ had not been proposed before and is formulated in a clausal-like manner, which eases its understanding, formal proofs and future extension towards non-clausal resolution.Thirdly, we prove that computing the inconsistency degree of H Σ members takes polynomial time. Although there already exist tractable classes in possibilistic logic, all of them are clausal, and thus, H Σ turns out to be the first characterized polynomial non-clausal class within possibilistic reasoning.We discuss that our approach serves as a starting point to developing uncertain non-clausal reasoning on the basis of both methodologies: DPLL and resolution.

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A Crash Course on Generalized Possibilistic Logic

Cited by 8 publications

References 27 publications

Computing a Possibility Theory Repair for Partially Preordered Inconsistent Ontologies

Computing a Possibility Theory Repair for Partially Preordered Inconsistent Ontologies

Possibility Theory and Possibilistic Logic: Tools for Reasoning Under and About Incomplete Information

The Possibilistic Horn Non-Clausal Knowledge Bases

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