Intuitionistic propositional probability logic

Ilić‐Stepić, Anelina; Knežević, Mateja; Ognjanović, Zoran

doi:10.1002/malq.202100052

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2023

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“…The concrete semantics of the modality can be defined in two ways. First, using a modal language with Kripke semantics where the measure is defined on the set of states as done in, e.g., [17,10,11] for qualitative probabilities and in [24] for the quantitative ones. Second, employing a two-layered formalism (cf.…”

Section: Introductionmentioning

confidence: 99%

Two-layered logics for paraconsistent probabilities

Bílková¹,

Frittella²,

Kozhemiachenko³

et al. 2023

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We discuss two two-layered logics formalising reasoning with paraconsistent probabilities that combine the Lukasiewicz [0, 1]-valued logic with Baaz △ operator and the Belnap-Dunn logic. The first logic Pr L 2 △ (introduced in [7]) formalises a 'two-valued' approach where each event φ has independent positive and negative measures that stand for, respectively, the likelihoods of φ and ¬φ. The second logic 4Pr L △ that we introduce here corresponds to 'four-valued' probabilities. There, φ is equipped with four measures standing for pure belief, pure disbelief, conflict and uncertainty of an agent in φ. We construct faithful embeddings of 4Pr L △ and Pr L 2 △ into one another and axiomatise 4Pr L △ using a Hilber-style calculus. We also establish the decidability of both logics and provide complexity evaluations for them using an expansion of the constraint tableaux calculus for L.

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