We present a duality for non-necessarily-distributive (modal) lattices and use this to study non-necessarily-distributive positive (modal) logic. Our duality is similar to Priestley duality and as such allows us to use similar tools and techniques to study logic. As a result, we prove Sahlqvist correspondence and canonicity for both the propositional logic as well as a modal extension.
翻译:我们提出了非必要分配(现代)暂存器的双重性,并利用它来研究非必要分配(现代)正(现代)逻辑。 我们的双重性类似于皮斯利的双重性,因此使我们能够使用类似的工具和技术来研究逻辑。 因此,我们证明了萨勒维斯特的通信和教义性,这既是为了理论逻辑,也是为了模式延伸。