Publications de l’Institut Mathématique, Nouvelle Série Vol. 100[114], No. 1/1, pp. 77–86 (2016) 

INFERENCE RULES FOR PROBABILITY LOGICMarija BoričićFaculty of Organizational Sciences, University of Belgrade, Belgrade, SerbiaAbstract: Gentzen’s and Prawitz’s approach to deductive systems, and Carnap’s and Popper’s treatment of probability in logic were two fruitful ideas of logic in the midtwentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized by means of inference rules, we introduce a system of inference rules based on the traditional prooftheoretic principles enabling to work with each form of probabilized propositional formulae. Namely, for each propositional connective, we define at least one introduction and one elimination rule, over the formulae of the form $A[a,b]$ with the intended meaning that ’the probability $c$ of truthfulness of a sentence $A$ belongs to the interval $[a,b]\subseteq [0,1]$’. It is shown that our system is sound and complete with respect to the Carnap–Popertype probability models. Keywords: consistency; inference rules; probability; soundness; completeness Classification (MSC2000): 03B48; 03B50; 03B05 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.
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