On Basic Probability Logic Inequalities

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