Propositions Formalized in Chu Spaces
Studies in Logic, Vol. 17, No. 6 (2024): 42–58 PII: 16743202(2024)06004217
Shengyang Zhong
Abstract. In the literature, there are many relational semantics of propositional logics each of which, although a satisfaction relation is defined, seems to have a “many-valued” intuition behind. More precisely, this means that a proposition can take one of more than two “truth values” at a state. In this paper, we use a kind of mathematical structures called Chu spaces to model such intuition; and we choose possibility semantics of classical logic, ortho-logic and Holliday’s fundamental logic to do case studies. We formalize some informal reasonings about the intuition behind the relational semantics of these three logics, make explicit the underlying assumptions and discover some new consequences of the intuition behind these relational semantics in our setting.