An Axiomatisation for the Multi-modal Logic of Knowledge and Linear Time LTK

The paper aims at providing the multi-modal propositional logic LTK with a sound and complete axiomatisation. This logic combines temporal and epistemic operators and focuses on m odeling the behaviour of a set of agents operating in a system on the background of a temporal framework. Time is represented as linear and discrete, whereas knowledge is modeled as an S5-like modality. A further modal operator intended to represent environment knowledge is added to the system in order to achieve the expressive power sufficient to describe the piece of information available to the agents at each moment in the flow of time.