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Discrete duality for lattices with modal operators

机译:具有模态算子的晶格的离散对偶

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It has been argued that in the context of automated theorem proving deduction procedures based on a frame semantics is more efficient than those based on algebraic semantics, for some logics. Frame semantics, for several logics, is specified by means of a representation and Stone-type duality result, involving a topology on the frame which, however, is not relevant in proving soundness of the logic. This has led to the development of a research program on Discrete Dualities, where a number of relevant results have been published over the past decade, but the program seems to have stumbled on the case of frames for non-distributive logics and bounded lattices with operators. In this article, we fill in this gap by presenting discrete dualities for bounded lattices and for lattices with one-place modal operators. Our results are extendible to discrete dualities for any normal lattice expansion.
机译:有人认为,在自动定理的证明中,对于某些逻辑,基于框架语义的推论程序要比基于代数语义的推论程序更有效。对于几种逻辑,框架语义是通过表示形式和Stone-type对偶结果指定的,该结果涉及框架上的拓扑,但是与证明逻辑的合理性无关。这导致了关于离散对偶的研究程序的开发,在过去的十年中已经发表了许多相关的结果,但是该程序似乎偶然发现了非分布逻辑的框架和带有算子的有界格架。在本文中,我们通过为有界晶格和具有一处模态算子的晶格提供离散对偶性来填补这一空白。对于任何正常晶格展开,我们的结果可扩展到离散对偶。

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