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Kripke Semantics for Intuitionistic Łukasiewicz Logic

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In this talk I’ll present a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Łukasiewicz logic IŁL – a logic in the intersection between IL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009) to show the decidability (and PSPACE -completeness) of the quasiequational theory of commutative, integral and bounded GBL -algebras. The main idea is that w⊩ψ – which for IŁL is a relation between worlds w and formulas ψ, and can be seen as a function taking values in the Booleans, i.e. (w⊩ψ)∈𝔹 – becomes a function taking values in the unit interval, i.e. (w⊩ψ)∈[0,1]. An appropriate monotonicity restriction needs to be put on such functions (which we then call sloping functions) in order to ensure soundness and completeness of the semantics. Based on paper [1], joint work with Andrew Lewis-Smith and Edmund Robinson.


[1] A. Lewis-Smith, P. Oliva, E. Robinson, Kripke Semantics for Intuitionistic Łukasiewicz Logic. Studia Logica, 109:313–339, 2021.

This talk will be chaired by Martin Escardo.

This talk is part of the Theoretical computer science seminar series.

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