Temporal Logics Modeling Logical Uncertainty, Local and Global Chance Discovery

Abstract

The paper develops a logical framework for studying Chance Discovery and Uncertainty. We investigate a special linear temporal logic \({\cal T}{\cal L}^{\cal Z}_{{\cal D}{\cal U}}\) with operations UNTIL and NEXT, which combines operations of the linear temporal logic LTL, the operation for discovery (variations of chance discovery – CD) and operation for logical uncertainty. We distinguish local and global discovery using approach of temporal logic. Our main aim is to solve problems of satisfiability and decidability for \({\cal T}{\cal L}^{\cal Z}_{{\cal D}{\cal U}}\). Our principal result is found algorithm which checks if any given formula is true in \({\cal T}{\cal L}^{\cal Z}_{{\cal D}{\cal U}}\) (which implies that \({\cal T}{\cal L}^{\cal Z}_{{\cal D}{\cal U}}\) is decidable, and the satisfiability problem for \({\cal T}{\cal L}^{\cal Z}_{{\cal D}{\cal U}}\) is solvable). In the final part of the chapter we consider the case of non-linear temporal logics based on just reflexive and transitive time flow (which does not implement operations UNTIL and NEXT) with interpretations of Chance Discovery and Uncertainty. Such logics are also decidable.Keywordslinear temporal logicchance discoveryuncertaintydecidability algorithmsKripke/Hintikka models