Multi-Agent Temporal Nontransitive Linear Logics and the Admissibility Problem

We study an extension of temporal logic, a multi-agent logic on models with nontransitive linear time (which is, in a sense, also an extension of interval logic). The proposed relational models admit lacunas in admissibility relations among agents: information accessible for one agent may be inaccessible for others. A logical language uses temporary operators ‘until’ and ‘next’ (for each of the agents), via which we can introduce modal operations ‘possible’ and ‘necessary.’ The main problem under study for the logic introduced is the recognition problem for admissibility of inference rules. Previously, this problem was dealt with for a logic in which transitivity intervals have a fixed uniform length. Here the uniformity of length is not assumed, and the logic is extended by individual temporal operators for different agents. An algorithm is found which decides the admissibility problem in a given logic, i.e., it recognizes admissible inference rules.