Model Checking Epistemic Halpern-Shoham Logic Extended with Regular Expressions

The Epistemic Halpern-Shoham logic (EHS) is a temporalepistemic logic that combines the interval operators of the HalpernShoham logic with epistemic modalities. The semantics of EHS is based on interpreted systems whose labelling function is defined on the endpoints of intervals. We show that this definition can be generalised by allowing the labelling function to be based on the whole interval by means of regular expressions. We prove that all the positive results known for EHS, notably the attractive complexity of its model checking problem for some of its fragments, still hold for its generalisation. We also propose the new logic EHS which operates on standard Kripke structures and has expressive power equivalent to that of EHS with regular expressions. We compare the expressive power of EHS with standard temporal logics.