Suppes-style sequent calculus for probability logic. (1st October 2015)

• Record Type: Journal Article
• Authors: Boričić, Marija
• Is Part Of: Journal of logic and computation. Volume 27:Number 4(2017)
• Page Start: 1157
• Page End: 1168
• Publication Date: 2015-10-01
• Subjects: Deduction relation -- sequent calculus -- consistency -- probability -- soundness -- completeness; Logic programming -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; Computational complexity -- Periodicals; 005.115
• DOI: 10.1093/logcom/exv068
• Languages: English
• ISSNs: 0955-792X

Abstract

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.