A Multi-Valued Simplified Halpern–Shoham–Moszkowski Logic for Gradable Verifiability in Reasoning about Digital Circuits

In 1983, B. Moszkowski introduced a first interval-interpreted temporal logic system, the so-called Interval Temporal Logic (ITL), as a system suitable to express mutual relations inside intervals for reasonings about digital circuits. In 1991, Halpern and Shoham proposed a new temporal system (HS) to describe external relations between intervals. This paper is aimed at proposing a basis-type combination of HS and a simplified ITL end extends it towards a multi-valued system—also capable of rendering a gradable justification of agents in a similar contexts of reasoning about digital circuits. This newly introduced system is semantically interpreted in the so-called fibred semantics.