An Epistemic Halpern-Shoham Logic for Gradable Justification

The Allen's relations between temporal intervals found its logical representation in terms of the so-called Halpern-Shoham logic (HS). This system forms a modal-type logic interpreted in the interval-based Kripke semantics. Unfortunately, not all phenomena of temporal reasoning may be rendered by HS. In 2013, an epistemic extension of HS was proposed by A. Lomuscio. In this paper a new epistemic Halpern-Shoham logic - as a system of multi-valued logic - for gradable justification is proposed. This system is semantically interpreted in the so-called fibred semantics, enriched by some elements of the so-called behavioral semantics of Fagin. The subject basis of the analysis is determined by a unique epistemic version of Traveling Salesman Problem in this paper.