Conditional Preference Nets and Possibilistic Logic

Abstract. This paper presents first results toward the extension of possibilistic logic when the total order on formulas is replaced by a partial preorder. Few works have dealt with this matter in the past but they include some by Halpern, and Benferhat et al. Here we focus on semantic aspects, namely the construction of a partial order on interpretations from a partial order on formulas and conversely. It requires the capability of inducing a partial order on subsets of a set from a partial order on its elements. The difficult point lies in the fact that equivalent definitions in the totally ordered case are no longer equivalent in the partially ordered one. We give arguments for selecting one approach extending comparative possibility and its preadditive refinement, pursuing some previous works by Halpern. It comes close to non-monotonic inference relations in the style of Kraus Lehmann and Magidor. We define an intuitively appealing notion of closure of a partially ordered belief base from a semantic standpoint, and show its limitations in terms of expressiveness, due to the fact that a partial ordering on subsets of a set cannot be expressed by means of a single partial order on the sets of elements. We also discuss several existing languages and syntactic inference techniques devised for reasoning from partially ordered belief bases in the light of this difficulty. The long term purpose is to find a proof method adapted to partially ordered formulas, liable of capturing a suitable notion of semantic closure.

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“…This work has potential applications for the revision and the fusion of beliefs, as well as preference modeling [29].…”

Section: Resultsmentioning

confidence: 99%

On the Semantics of Partially Ordered Bases

Cayrol

Dubois

Touazi

2014

Lecture Notes in Computer Science

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“…As shown in [5], for vectors of the form ω(Σ N ), the discrimin and leximin orderings coincide, because the coefficients 1 − α i in different components always differ. It was claimed in [6] that the above possibilistic logic encoding of a CP-net can exactly capture the CP-net ordering (defined in terms of worsening flips, as recalled at the beginning of this note) using the leximin (or discrimin) order for comparing vectors associated to interpretations of the corresponding possibilistic base.…”

Section: The Leximin Comparison Comes Down To Deleting All Pairsmentioning

confidence: 98%

“…Unfortunately, this is true only for particular CP-nets. In actual fact, results in [5] suggest it may only provide a refinement of the CP-net ordering of solutions, namely, let N be an acyclic CP-net and N its induced partial preference ordering on interpretations. Then, it can be conjectured that…”

Section: The Leximin Comparison Comes Down To Deleting All Pairsmentioning

confidence: 99%

Erratum to: Database preference queries - a possibilistic logic approach with symbolic priorities

Dubois

Hadjali

Prade

et al. 2015

Ann Math Artif Intell

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This note corrects a claim made in the above-mentioned paper about the exact representation of a conditional preference network by means of a possibilistic logic base with partially ordered symbolic weights. We provide a counterexample that shows that the possibilistic logic representation is indeed not always exact. This is the basis of a short discussion on the difficulty of obtaining an exact representation. This note corrects a claim made in [6] about the representation of Conditional Preference networks (CP-nets for short) [1] by means of a possibilistic logic base [2], as well as a similar claim in [7, 8]. A CP-net encodes a set of preference statements concerning the values of Boolean decision variables, conditioned on the values of other Boolean decision variables that influence the former. More formally, let V = {X 1 , • • • , X n } be a set of Boolean variables. We denote by Ast (S) the set of interpretations of variables of S (⊆ V). Definition 1 A CP-net N over V = {X 1 , • • • , X n } is a directed graph with nodes X 1 , • • • , X n , and there is a directed edge from X i to X j if the preference about the value X j depends on the value of X i. Each node X i ∈ V is associated with a conditional preference table CP T i that associates a strict preference (x i > ¬x i or ¬x i > x i

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“…It enables constraints over weights to be taken into account so as to simplify the comparison of symbolic necessity degrees. This work has potential applications for the revision and the fusion of beliefs, as well as preference modeling [14].…”

Section: Related Workmentioning

confidence: 99%

Symbolic Possibilistic Logic: Completeness and Inference Methods

Cayrol

Dubois

Touazi

2015

Lecture Notes in Computer Science

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15404The contribution was presented at ECSQARU 2015 :https://ecsqaru2015.hds.utc.fr/ Abstract. This paper studies the extension of possibilistic logic to the case when weights attached to formulas are symbolic and stand for variables that lie in a totally ordered scale, and only partial knowledge is available on the relative strength of these weights. A proof of the soundness and the completeness of this logic according to the relative certainty semantics in the sense of necessity measures is provided. Based on this result, two syntactic inference methods are presented. The first one calculates the necessity degree of a possibilistic formula using the notion of minimal inconsistent sub-base. A second method is proposed that takes inspiration from the concept of ATMS. Notions introduced in that area, such as nogoods and labels, are used to calculate the necessity degree of a possibilistic formula. A comparison of the two methods is provided, as well as a comparison with the original version of symbolic possibilistic logic.

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Conditional Preference Nets and Possibilistic Logic

Cited by 11 publications

References 10 publications

On the Semantics of Partially Ordered Bases

On the Semantics of Partially Ordered Bases

Erratum to: Database preference queries - a possibilistic logic approach with symbolic priorities

Symbolic Possibilistic Logic: Completeness and Inference Methods

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