On Rational Entailment for Propositional Typicality Logic

in Artificial Intelligence and Law (in press)

Propositional Typicality Logic (PTL) is a recently proposed logic, ob- tained by enriching classical propositional logic with a typicality opera- tor capturing the most typical (alias normal or ... [more ▼]

Propositional Typicality Logic (PTL) is a recently proposed logic, ob- tained by enriching classical propositional logic with a typicality opera- tor 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 preferen- tial 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 impossibil- ity 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 in- vestigate 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. [less ▲]

Extending Typicality for Description Logics

Report (2017)

Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a ... [more ▼]

Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a (constrained version of) a typicality operator •, the intuition of which is to capture the most typical members of a class, providing us with the DL EL•⊥. We argue that EL•⊥ is the smallest step one can take to increase the expressivity beyond the case of defeasible subsumption for DLs, while still retaining all the rationality properties an appropriate notion of defeasible subsumption is required to satisfy, and investigate what an appropriate notion of non-monotonic entailment for EL•⊥ should look like. [less ▲]

DARe-16 - Proceedings of the International Workshop on Defeasible and Ampliative Reasoning

Book published by CEUR Workshop Proceedings (2016)

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-16), co-located with the 22th European Conference on Artificial Intelligence (ECAI 2016). The Hague, Holland, August ... [more ▼]

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-16), co-located with the 22th European Conference on Artificial Intelligence (ECAI 2016). The Hague, Holland, August 29, 2016. [less ▲]