Reasoning about inconsistent concurrent systems: a non-classical temporal logic

It has been widely recognized that inconsistencies often appear and are inevitable when specifying large and complex concurrent systems. The logic QCL (quasi-classical logic) has therefore been developed for handling such specifications. But, on the one hand, temporal aspects, significant for ensuring the correct behavior of concurrent systems, cannot be specified by QCL, on the other hand, Classical temporal logics like CTL (computation tree logic) fail for system specifications with inconsistent information due to the trivial inference problem. To bridge this gap, in this paper a non-classical temporal logic QCTL (quasi-classical temporal logic) is introduced, including a novel semantics in term of paraKripke structures and a sound and complete proof system. It is paraconsistent, i.e., it can be used to non-trivially reason about inconsistent system specifications. Furthermore, an example is presented, showing the use of QCTL for reasoning about concurrent systems containing inconsistent information.