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Linear and affine logics with temporal, spatial and epistemic operators

机译：具有时间，空间和认知运算符的线性和仿射逻辑

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摘要

A temporal spatial epistemic intuitionistic linear logic (TSEILL) is introduced, and the completeness theorem for this logic is proved with respect to Kripke semantics. TSEILL has three temporal modal operators: [F] (any time in the future), [N] (next time) and [P] (past), some spatial modal operators [l{sub}i] (locations), two epistemic modal operators; [K] (know) and (K}, and a linear modal operator ! (exponential). A basic normal modal intuitionistic affine logic (BIAL) and its normal extensions are also defined, and the completeness theorems for these logics are proved with respect to Kripke semantics. In the proposed semantic framework of these normal extensions, a simple correspondence can be given between frame conditions and Lemmon-Scott axioms. A dynamic intuitionistic affine logic (DIAL) is proposed as an affine version of (test-free) dynamic logic, and the completeness theorem for this logic is shown with respect to Kripke semantics. Finally, some intuitive interpretations, such as resource and informational interpretations, are given for the proposed logics and semantics. By using these logics, semantics and interpretations, various kinds of fine-grained resource-sensitive reasoning can be expressed.
机译：介绍了一种时空的认知直觉线性逻辑（TSEILL），并针对Kripke语义证明了该逻辑的完备性定理。 TSEILL具有三个时间模态运算符：[F]（将来的任何时间），[N]（下一时间）和[P]（过去），一些空间模态运算符[l {sub} i]（位置），两个认知模态运算符; [K]（know）和（K}，以及线性模态运算符！（指数），还定义了基本的正规模态直觉仿射逻辑（BIAL）及其正态扩展，并针对这些逻辑证明了完备性定理在正常扩展的语义框架中，可以给出框架条件与Lemmon-Scott公理之间的简单对应关系，并提出了动态直觉仿射逻辑（DIAL）作为（免测试）动态的仿射版本。逻辑，并针对Kripke语义给出了该逻辑的完备性定理，最后，针对所提出的逻辑和语义给出了一些直观的解释，例如资源和信息解释，通过这些逻辑，语义和解释，可以使用各种逻辑可以表示细粒度的资源敏感推理。

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