论文标题
兼容性和可访问性：非古典和模态逻辑语义的晶格表示
Compatibility and accessibility: lattice representations for semantics of non-classical and modal logics
论文作者
论文摘要
在本文中，我们通过在Ploščica传统中与兼容性二进制关系的集合研究了三种晶格的表示。完整的矫形器的标准表示和完整的完美Heyting代数作为第一个表示的特殊情况，而第二个代数则覆盖了任意完整的晶格，以及配备有否定的完整晶格，我们称之为触发。第三个拓扑表示是Craig，Haviar和Priestley的变体。然后，我们将三个表示中的每一个都扩展到具有乘法一元模态的晶格。代表结构，例如所谓的基于图的帧，添加了与兼容性相互作用的第二个关系。这三个表示将经典模态逻辑的可能性语义推广到非古典模态逻辑，这是由于最新的模态正交学到自然语言语义的应用。
In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then extend each of the three representations to lattices with a multiplicative unary modality; the representing structures, like so-called graph-based frames, add a second relation of accessibility interacting with compatibility. The three representations generalize possibility semantics for classical modal logics to non-classical modal logics, motivated by a recent application of modal orthologic to natural language semantics.
