Semantics for Dual Preferential Entailment

Britz, Katarina; Heidema, Johannes; Labuschagne, WA

doi:10.1007/s10992-008-9097-z

Cited by 10 publications

(9 citation statements)

References 11 publications

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“…In our setup, the preference relation ≺ is on Tok(W ) and we will use it to spawn a ≺ relation on Typ(W ). We choose to use the preferential entailment relation defined in [3,11]. They use what is called a rational entailment relation., ϕ |∼ ψ.…”

Section: Preferential Entailmentsmentioning

confidence: 99%

“…This relation is induced by the semantics for preferential entailment. One cautionary note, [3] have used the converse of the preference relations in [11]. It is merely a matter of taste and we follow [3]; x ≺ y if one prefers y to x.…”

Section: Preferential Entailmentsmentioning

confidence: 99%

“…We will follow [3] in using x |= W ϕ for the valuation l(x) satisfying ϕ. The semantics of the preferential consequence relation relies on maximal tokens in the Tok(ϕ), where Tok(ϕ) is the set {x | x ∈ Tok(W ) and x |= W ϕ}, for proposition ϕ.…”

Section: Iff R(s) < R(t)mentioning

confidence: 99%

“…Using Joyce's [9] rendition of Savage's work, we show a consequence relation connecting states and outcomes of actions satisfying Joyce's criteria for such a consequence relation. We do not adopt Savage's restrictions on preferences but instead adopt the preference relations for preferential entailment [3,11,10,5]. We show that this preferential entailment satisfies many of the properties Joyce asserts for a proper conditional.…”

Section: Introductionmentioning

confidence: 99%

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Qualitative decision theory via channel theory

Allwein

Yang

Harrison

2013

LLP

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Abstract. We recast parts of decision theory in terms of channel theory concentrating on qualitative issues. Channel theory allows one to move between model theoretic and language theoretic notions as is necessary for an adequate covering. Doing so clarifies decision theory and presents the opportunity to investigate alternative formulations. As an example, we take some of Savage's notions of decision theory and recast them within channel theory. In place of probabilities, we use a particular logic of preference. We introduce a logic for describing actions separate from the logic of preference over actions. The structures introduced by channel theory that represent the decision problems can be seen to be an abstract framework. This framework is very accommodating to changing the nature of the decision problems to handle different aspects or theories about decision making.

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Section: Preferential Entailmentsmentioning

confidence: 99%

Section: Preferential Entailmentsmentioning

confidence: 99%

Section: Iff R(s) < R(t)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Qualitative decision theory via channel theory

Allwein

Yang

Harrison

2013

LLP

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“…In a previous paper [6], we presented a general preferential semantic framework for defeasible subsumption in description logics, analogous to the KLM preferential semantics for propositional entailment [5,19]. We gave a formal semantics of defeasible subsumption, as well as a translation of defeasible subsumption to classical subsumption within a suitably rich DL language.…”

Section: Introductionmentioning

confidence: 99%

Modelling Object Typicality in Description Logics

Britz

Heidema

Meyer

2009

AI 2009: Advances in Artificial Intelligence

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Abstract. We present a semantic model of typicality of concept members in description logics that accords well with a binary, globalist cognitive model of class membership and typicality. We define a general preferential semantic framework for reasoning with object typicality in description logics. We propose the use of feature vectors to rank concept members according to their defining and characteristic features, which provides a modelling mechanism to specify typicality in composite concepts.

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A KLM Perspective on Defeasible Reasoning for Description Logics

Britz¹,

Casini²,

Meyer³

et al. 2019

Lecture Notes in Computer Science

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In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more eective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption. 5 Keywords: Knowledge representation and reasoning • description logics • defeasible reasoning • preferential semantics. Given C, D ∈ L, C D is called a subsumption statement, or general concept inclusion (GCI). C ≡ D is an abbreviation for both C D and D C. An 6 Given X ⊆ ∆ P , with min ≺ P X we denote the set {x ∈ X | for every y ∈ X, y ≺ P x}.

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Semantics for Dual Preferential Entailment

Cited by 10 publications

References 11 publications

Qualitative decision theory via channel theory

Qualitative decision theory via channel theory

Modelling Object Typicality in Description Logics

A KLM Perspective on Defeasible Reasoning for Description Logics

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