Suppes-style sequent calculus for probability logic. (1st October 2015) - Boričić, Marija
Abstract: In order to treat the deduction relation ⊢ in the context of probabilistic reasoning, we introduce a system L K p r o b ( ε ) making it possible to work with expressions of the form Γ ⊢ n Δ, a generalization of Gentzen's sequents Γ ⊢ Δ of classical propositional logic L K, with the intended meaning that 'the probability of the sequent Γ ⊢ Δ is greater than or equal to 1 − n ε ', for a given small real ε > 0 and any natural number n . The system L K p r o b ( ε ) can be considered a program inferring a conclusion of the form Γ ⊢ n A from a finite set of hypotheses of the same form Γ i ⊢ n i A i ( 1 ≤ i ≤ n ) . We prove that our system is sound and complete with respect to the Carnap–Popper–type probability models.