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 ▲]

Taking Defeasible Entailment beyond Rational Closure

in Proceedings of the 16th European Conference on Logics in Artificial Intelligence (JELIA-19) (2019)

We present a systematic approach for extending the KLM framework for defeasible entailment. We first present a class of basic defeasible entailment relations, characterise it in three distinct ways and ... [more ▼]

We present a systematic approach for extending the KLM framework for defeasible entailment. We first present a class of basic defeasible entailment relations, characterise it in three distinct ways and provide a high-level algorithm for computing it. This framework is then refined, with the refined version being characterised in a similar manner. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our refined framework, that rational closure is the most conservative of the defeasible entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible entailment within our framework that are more “adventurous” than lexicographic closure. [less ▲]

A Semantic Perspective on Belief Change in a Preferential Non-Monotonic Framework

in Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2018) (2018)

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the ... [more ▼]

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the integration of the two formalisms by studying belief change for a (preferential) non-monotonic framework. We show that the standard AGM approach to be- lief change can be transferred to a preferential non-monotonic framework in the sense that change operations can be defined on conditional knowledge bases. We take as a point of depar- ture the results presented by Casini and Meyer (2017), and we develop and extend such results with characterisations based on semantics and entrenchment relations, showing how some of the constructions defined for propositional logic can be lifted to our preferential non-monotonic framework. [less ▲]

On Rational Entailment for Propositional Typicality Logic

Report (2018)

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 ... [more ▼]

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. [less ▲]

DARe-17 - Proceedings of the Fourth International Workshop on Defeasible and Ampliative Reasoning

Book published by CEUR Workshop Proceedings (2017)

Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning (DARe-17), co-located with the 14th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-17 ... [more ▼]

Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning (DARe-17), co-located with the 14th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-17). Espoo, Finland, July 3—6, 2017. [less ▲]

On the Entailment Problem for a Logic of Typicality

in Yang, Qiang; Wooldridge, Michael (Eds.) Proceedings of the TwentyFourth International Joint Conference on Artificial Intelligence. Buenos Aires, Argentina, 25–31 July 2015 (2015)

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. In spite of the non-monotonic features introduced by the ... [more ▼]

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. 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. We investigate different (semantic) versions of entailment for PTL, based on the notion of Rational Closure as defined by Lehmann and Magidor for KLM-style conditionals, and constructed using minimality. 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 define two primary forms of entailment for PTL and discuss their advantages and disadvantages. [less ▲]

Proceedings of the 2nd International Workshop on Defeasible and Ampliative Reasoning (DARe-15)

Book published by CEUR Workshop Proceedings (2015)

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-15), co-located with the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015). Buenos Aires ... [more ▼]

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-15), co-located with the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015). Buenos Aires, Argentina, July 27, 2015. [less ▲]