Informational logic in knowledge representation and automated deduction

Informational logic is a new approach to the formalization of the notion of rational conjecture that is of interest both from the epistemic and the automated reasoning point of view. Given a logical system $T$ , an informational logic is based on a new measure of logical information (which is defined on $T$ ‐formulas) and on a mathematical definition of estimate criteria for proofs in $T$ . This allows us to obtain a notion of informational theorem $(L,p(L))$ of a system $T$ , where $p(L)$ is the probability of $L$ to be provable in $T$ . The notion of probability is entirely founded on proof‐theoretic concepts. In this paper, informational logic is presented, and applications of this idea to the representation of inductive reasoning and to automated theorem proving are shown.