Booth, RCasini, GMeyer, TVarzinczak, I2016-02-232016-02-232015-07Booth, R, Casini, G, Meyer, T and Varzinczak, I. 2015. On the entailment problem for a logic of typicality. IJCAI'15 Proceedings of the 24th International Conference on Artificial Intelligence, Buenos Aires, Argentina, 25-31 July 2015http://ksg.meraka.org.za/~tmeyer/conferences/2015-IJCAI.pdfhttp://dl.acm.org/citation.cfm?id=2832641http://hdl.handle.net/10204/8381IJCAI'15 Proceedings of the 24th International Conference on Artificial Intelligence, Buenos Aires, Argentina, 25-31 July 2015. Due to copyright restrictions, the attached PDF file only contains the abstract of the full text item. For access to the full text item, please consult the publisher's websitePropositional 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.enEntailmentKLM-StylePropositional Typicality LogicPTLConference PresentationBooth, R., Casini, G., Meyer, T., & Varzinczak, I. (2015). On the entailment problem for a logic of typicality. AAAI Press. http://hdl.handle.net/10204/8381Booth, R, G Casini, T Meyer, and I Varzinczak. "On the entailment problem for a logic of typicality." (2015): http://hdl.handle.net/10204/8381Booth R, Casini G, Meyer T, Varzinczak I, On the entailment problem for a logic of typicality; AAAI Press; 2015. http://hdl.handle.net/10204/8381 .TY - Conference Presentation AU - Booth, R AU - Casini, G AU - Meyer, T AU - Varzinczak, I AB - 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. DA - 2015-07 DB - ResearchSpace DP - CSIR KW - Entailment KW - KLM-Style KW - Propositional Typicality Logic KW - PTL LK - https://researchspace.csir.co.za PY - 2015 T1 - On the entailment problem for a logic of typicality TI - On the entailment problem for a logic of typicality UR - http://hdl.handle.net/10204/8381 ER -