Typology of Axioms for a Weighted Modal Logic

Abstract : This paper introduces and studies extensions of modal logics by investigating the soundness of classical modal axioms in a weighted framework. It discusses the notion of relevant weight values, in a specific weighted Kripke semantics and exploits accessibility relation properties. Different generalisations of the classical axioms are constructed and, from these, a typology of weighted axioms is built, distinguishing between four types, depending on their relations to their classical counterparts and to the, possibly equivalent, frame conditions.
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https://hal.sorbonne-universite.fr/hal-01558038
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Submitted on : Friday, September 29, 2017 - 3:23:09 PM
Last modification on : Thursday, March 21, 2019 - 1:10:41 PM

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Bénédicte Legastelois, Marie-Jeanne Lesot, Adrien Revault d'Allonnes. Typology of Axioms for a Weighted Modal Logic. International Journal of Approximate Reasoning, Elsevier, 2017, 90, pp.341-358. ⟨10.1016/j.ijar.2017.06.011⟩. ⟨hal-01558038⟩

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