This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an event and its complement need not be the top element. Nonetheless, behavior is locally governed by the laws of propositional logic. By further endowing these structures with operators -- akin to the theory of modal Algebras -- RBAs serve as models of modal logics in which truth is relative. In particular, modal RBAs provide semantics for various well known awareness logics and an alternative view of possibility semantics.

翻译：本文列出了一组代数结构,即相对化的布尔代数(RBAs),这些代数结构为假设逻辑提供了语义,其中仅根据当地域界定真相/有效性,特别是,一个事件的结合及其补充不一定是最高要素。然而,行为由当地根据假设逻辑法则加以规范。通过进一步将这些结构与操作者联系起来 -- -- 类似于模式代数理论 -- -- RBAs作为模型逻辑模型的模型,其中真理是相对的。特别是,模式RBAs为各种众所周知的认知逻辑提供了语义,并提出了对可能性语义的替代观点。