{"type":"ScholarlyArticle","title":"On the Entailment Problem for a Logic of Typicality","authors":[{"name":"Richard Booth","slug":"richard-booth","given":"Richard","family":"Booth","affiliation":""},{"name":"Giovanni Casini","slug":"giovanni-casini","given":"Giovanni","family":"Casini","affiliation":""},{"name":"Thomas Andreas Meyer","slug":"thomas-andreas-meyer","given":"Thomas Andreas","family":"Meyer","affiliation":""},{"name":"Ivan José Varzinczak","slug":"ivan-jose-varzinczak","given":"Ivan José","family":"Varzinczak","affiliation":""}],"abstract":"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 satis- fied 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.","doi":null,"url":"https://ijcai.org/proceedings/2015/397","pdf":"https://ijcai.org/proceedings/2015/0397.pdf","markdown":"https://ijcai.org/proceedings/2015/397.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/397","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Special Track on Knowledge Representation and Reasoning","track":"Special Track on Knowledge Representation and Reasoning","number":397,"pages":{"first":2805,"last":2810},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}