Logic of knowledge and discovery via interacting agents – Decision algorithm for true and satisfiable statements

In this paper we study logical properties of the operation chance discovery (CD) via structures based on special Kripke/Hintikka models. These models use as bases partially ordered sets of indexes (indexes of steps in a computation, or ones indicating time points in a time flow), and clusters of states associated to each index. The language chosen to build the logical formulas includes modal/temporal operations, operations for the agents’ knowledge, local and global operations for CD, operation of local common knowledge, and an operation for chance of discovery via agents’ interactions. We introduce and study a logic (of knowledge and discovery via interaction of agents), LDKa, which is defined by semantics, as the set of all formulas that are valid in all suggested models. The paper provides an algorithm to recognize logical laws (and satisfiable formulas) of LDKa. The algorithm replaces a formula with a rule in a special, so-called reduced normal form, and, then it verifies the validity of this rule in specific models of exponential size in the size of the rule. We show that the problem of computing the true logical laws of LDKa is decidable.