We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We establish fascinating connections between the original semantics based on multisets and the new set-based semantics as well as show one of the first positive complexity theoretic results in the temporal team semantics setting. In particular we show that both logics enjoy normal forms that can be utilised to obtain results related to expressivity and complexity (decidability) of the new logics. We also relate and apply our results to recently defined logics whose asynchronicity is formalized via time evaluation functions.
翻译:我们引入并建立了异步TeamLTL的基于集合的语义。我们在这个设置中考虑了两个规范的逻辑:通过布尔或和通过布尔否定扩展的TeamLTL。我们建立了原始基于多重集的语义和新的基于集合的语义之间的有趣联系,并展示了时间团队语义设置中最早的正向复杂度理论结果之一。特别的,我们展示了这两个逻辑拥有能够用于获得有关新逻辑的表达能力和复杂度(可判定性)的结果的正常形式。我们还将我们的结果与最近通过时间评估函数形式化其异步性的定义的逻辑联系并应用。