On Basic Probability Logic Inequalities

Marija Boričić Joksimović
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Marija Boričić Joksimović: Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia

Mathematics, 2021, vol. 9, issue 12, 1-6

Abstract: We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A , B , C , A ? B , and B ? C have probabilities a , b , c , r , and s , respectively, then for probability p of A ? C , we have f ( a , b , c , r , s ) ? p ? g ( a , b , c , r , s ) , for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

Keywords: inequality; probability logic; inference rule (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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