Modelling Object Typicality in Description Logics

Britz, Katarina; Heidema, Johannes; Meyer, Thomas

doi:10.1007/978-3-642-10439-8_51

Cited by 7 publications

(5 citation statements)

References 26 publications

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“…The intuition underlying this is simple and natural, and extends similar work done for the propositional case by Shoham [73], Kraus et al [56], Lehmann and Magidor [59] and Booth et al [12,13,14] to the case for description logics. This is not the first extension of this kind, as evidenced by the work of Boutilier [16], Baltag and Smets [5,6], Giordano et al [46,48,49,50,51,52], Britz et al [19,20,21,22,24] and Britz and Varzinczak [26,27,30,29,31,32]. However, this is the first comprehensive semantic account of both preferential and rational subsumption relations, with accompanying representation results, based on the standard semantics for description logics.…”

Section: Preferential Semantics and Representation Resultsmentioning

confidence: 98%

“…Informally, our semantic constructions are based on the idea that objects of the domain can be ordered according to their degree of normality [16] or typicality [13,14,22,46]. Paraphrasing Boutilier [16, pp.…”

Section: Preferential Semantics and Representation Resultsmentioning

confidence: 99%

“…Indeed, the past 25 years have witnessed many attempts to introduce defeasible-reasoning capabilities in a DL setting, usually drawing on a well-established body of research on nonmonotonic reasoning (NMR). These comprise the so-called preferential approaches [21,22,24,37,40,46,47,51,52,66,67], circumscription-based ones [9,10,72], amongst others [2,3,8,43,53,54,55,62,65,74].…”

Section: Introductionmentioning

confidence: 99%

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Theoretical Foundations of Defeasible Description Logics

Britz,

Casini,

Meyer

et al. 2019

Preprint

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We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in DLs. Indeed, we also analyse the problem of non-monotonic reasoning in DLs at the level of entailment and present an algorithm for the computation of rational closure of a defeasible ontology. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of reasoning in the underlying classical DL ALC.

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Section: Preferential Semantics and Representation Resultsmentioning

confidence: 98%

Section: Preferential Semantics and Representation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theoretical Foundations of Defeasible Description Logics

Britz,

Casini,

Meyer

et al. 2019

Preprint

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“…Britz et al [6] and Giordano et al [16] have investigated the connection between the KLM approach and Gödel-Löb modal logic, which is closely related to PTL. Exploiting this connection should deliver an axiomatisation of an inference relation corresponding to ranked entailment, but it does not seem useful for modelling entailment relations based on minimisation as LM-and PT-entailment.…”

Section: Discussionmentioning

confidence: 99%

On rational entailment for Propositional Typicality Logic

Booth

Casini

Meyer

et al. 2019

Artificial Intelligence

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Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality. * This technical report presents an extended and elaborated version of a paper presented at the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015). Si is a ranked model of KB.Proof:So, at each stage of the algorithm, the current ranked interpretation, when those valuations not satisfying KB are excluded, forms a ranked model of KB. Since the output R * KB takes precisely this form we have the following result. Proposition 5.1 R * KB KB. Proof: Follows from Lemma 5.2 and the construction of R * KB . Next we want to show that for any other ranked model R of KB, we have R * KB LM R. Lemma 5.3 Let R * KB := (L 0 , . . . , L n−1 , L ∞ ) and let R := (M 0 , . . . , M n−1 , M ∞ ) be any other ranked model of KB.From this lemma we can state:Proposition 5.2 Consider any KB and let R be a ranked model of KB. Then R * KB LM R.We are now in a position to define our first form of entailment for PTL. Definition 5.2 (LM-entailment) Let KB ⊆ L • and α ∈ L • . We say KB LM-entails α, denoted KB |≈ LM α, if R * KB α. Its corresponding consequence operator is defined as Cn LM (KB) := {α ∈ L • | R * KB α}.The next result outlines which properties from the previous section are satisfied by Cn LM (·).Theorem 5.2 Cn LM (·) satisfies P1-P7, P9, and P10, but not P8. Proof:For P1, Proposition 5.1 guarantees that R * KB is a model of KB. About P2, by Proposition 5.2, R * KB is the LM-minimum model of KB. If R * KB α, R * KB must also be the LM-minimum model of KB ∪ {α}. For P3, note that R * KB is a ranked model of KB (Lemma 5.1, Item 3, plus Proposition 5.1), and so if α ∈ Cn 0 (KB), then α ∈ R * KB . P4 is an immediate consequence of the satisfaction of P7. 3 P5 is an immediate consequence of the satisfaction o...

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“…Further lines of research will deepen the comparison with the formal studies on typicality (e.g. [12,13,14]), the relation and combination with similarity frameworks based on a notion of distance (e.g. [15,16,17]), and the connections to linear classification models as begun in [8].…”

Section: Future Workmentioning

confidence: 99%

Weighted Description Logic for Classification Problems

Righetti¹,

Galliani²,

Kutz³

et al.

EPiC Series in Computing

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We summarise the definitions and some technical aspects of a familiy of description logics that introduce concept constructors (so-called tooth-operators) which, under various constraints, accumulate weights of concepts. We demonstrate how these operators can be fruitfully and elegantly applied to a number of cognitively motivated classification problems which are difficult to handle with the standard expressive means of description logics.

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Modelling Object Typicality in Description Logics

Cited by 7 publications

References 26 publications

Theoretical Foundations of Defeasible Description Logics

Theoretical Foundations of Defeasible Description Logics

On rational entailment for Propositional Typicality Logic

Weighted Description Logic for Classification Problems

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