Britz, KHeidema, JVarzinczak, I2010-09-302010-09-302010-05Britz, K, Heidema, J and Varzinczak, I. 2010. Pertinent reasoning. 13th International Workshop on Nonmonotonic Reasoning (NMR), Toronto, Canada, 14-16 May 2010, pp 7http://hdl.handle.net/10204/443013th International Workshop on Nonmonotonic Reasoning (NMR), Toronto, Canada, 14-16 May 2010In this paper the authors venture beyond one of the fundamental assumptions in the non-monotonic reasoning community, namely that non-monotonic entailment is supra-classical. They investigate reasoning which uses an infra-classical entailment relation that they call pertinent entailment. The notion of pertinence proposed here is induced by a binary accessibility relation on worlds establishing a link (representing some form of pertinence) between premiss and consequence. They show that this notion can be captured elegantly using a simple modal logic without nested modalities. One road to infra-classicality has been studied extensively, that of substructural logics, which weaken the generating engine of axioms and inference rules for producing entailment pairs (X; Y). Here they follow an alternative strategy: we first demand that X entails Y classically, and then, with supplementary information provided by an accessibility relation, more, trimming down the set of entailment pairs to infra-classicality. It turns out that pertinent entailment restricts well-known ‘paradoxes’ avoided by relevance/relevant logic in an interesting way. They present its properties, showing that it possesses other non-classical properties, like strong non-explosiveness and non-monotonicity, and we discuss which inference rules traditionally considered in the literature it satisfiesenNonmonotonic reasoningSupra-classicalInfra-classicalPertinent reasoningConference PresentationBritz, K., Heidema, J., & Varzinczak, I. (2010). Pertinent reasoning. http://hdl.handle.net/10204/4430Britz, K, J Heidema, and I Varzinczak. "Pertinent reasoning." (2010): http://hdl.handle.net/10204/4430Britz K, Heidema J, Varzinczak I, Pertinent reasoning; 2010. http://hdl.handle.net/10204/4430 .TY - Conference Presentation AU - Britz, K AU - Heidema, J AU - Varzinczak, I AB - In this paper the authors venture beyond one of the fundamental assumptions in the non-monotonic reasoning community, namely that non-monotonic entailment is supra-classical. They investigate reasoning which uses an infra-classical entailment relation that they call pertinent entailment. The notion of pertinence proposed here is induced by a binary accessibility relation on worlds establishing a link (representing some form of pertinence) between premiss and consequence. They show that this notion can be captured elegantly using a simple modal logic without nested modalities. One road to infra-classicality has been studied extensively, that of substructural logics, which weaken the generating engine of axioms and inference rules for producing entailment pairs (X; Y). Here they follow an alternative strategy: we first demand that X entails Y classically, and then, with supplementary information provided by an accessibility relation, more, trimming down the set of entailment pairs to infra-classicality. It turns out that pertinent entailment restricts well-known ‘paradoxes’ avoided by relevance/relevant logic in an interesting way. They present its properties, showing that it possesses other non-classical properties, like strong non-explosiveness and non-monotonicity, and we discuss which inference rules traditionally considered in the literature it satisfies DA - 2010-05 DB - ResearchSpace DP - CSIR KW - Nonmonotonic reasoning KW - Supra-classical KW - Infra-classical KW - Pertinent reasoning LK - https://researchspace.csir.co.za PY - 2010 T1 - Pertinent reasoning TI - Pertinent reasoning UR - http://hdl.handle.net/10204/4430 ER -