Non normal logics: semantic analysis and proof theory

Alessandra Palmigiano; Apostolos Tzimoulis; Giuseppe Greco; Jinsheng Chen

Non normal logics: semantic analysis and proof theory

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arxiv 1903.04868 v1 pith:4SFE2UMG submitted 2019-03-12 math.LO

Jinsheng Chen , Giuseppe Greco , Alessandra Palmigiano , Apostolos Tzimoulis This is my paper · ORCID

classification math.LO

keywords logiccalculianalysisdisplaymodalmonotonicnormalsemantic

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We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our proposal applies the multi-type methodology in the design of display calculi, starting from a semantic analysis based on the translation from monotonic modal logic to normal bi-modal logic.

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Vector spaces as Kripke frames
cs.LO 2019-08 accept novelty 7.0 of 10

Vector spaces equipped with a bilinear product are shown to form Kripke-style frames whose subspace lattices are complete residuated lattices, yielding a complete vector space semantics for the modal non-associative L...

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