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.

中文翻译：

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多代理时间非传递线性逻辑和可接受性问题

我们研究了时间逻辑的扩展，一种基于非传递线性时间模型的多智能体逻辑（从某种意义上说，也是区间逻辑的扩展）。提议的关系模型承认代理之间的可接纳关系存在缺陷：一个代理可访问的信息可能对其他人不可访问。逻辑语言使用临时运算符“直到”和“下一步”（对于每个代理），通过它们我们可以引入模态操作“可能”和“必要”。所引入的逻辑所研究的主要问题是推理规则的可接受性的识别问题。以前，此问题是针对传递间隔具有固定的统一长度的逻辑处理的。这里没有假设长度的一致性，并且逻辑由不同代理的各个时间运算符扩展。