Zoom Talk: Roberto Ciuni (Rome)
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Partial Information, Strong Kleene, and Intuitionistic Logic
Strong Kleene logic and the Kripke/Grzegorczyk interpretation of Intuitionistic Logic are motivated by a story of partial information. Following Michael Dunn, I argue that the Kripke/Grzegorczyk semantics and the 'partial information' story do not really go together well, and I propose an alternative semantical framework. This framework is able to generate a version of Strong Kleene that includes an intuitionistic conditional (thus fixing one weak point of the original Strong Kleene), a version of Intuitionistic Logic based on Strong Kleene, and Intuitionistic Logic itself (as a special case). The framework builds states of a frame as packs of positive and negative factual information. Two interesting consequences of this are that the heredity condition of the Kripke/Grzegorczyk semantics is somehow built in the frames, rather than imposed on the valuations, and that the 'partial information' reading is built in the framework, rather than imposed as an informal reading.