The Modal Logic of Aristotelian Diagrams

In this paper, we introduce and study AD-logic, i.e., a system of (hybrid) modal logic that can be used to reason about Aristotelian diagrams. The language LAD, is interpreted on kind birelational Kripke frames, which call “AD-frames”. We establish sound strongly complete axiomatization for prove there exists bijection between finite diagrams (up isomorphism) AD-frames isomorphism). then show how AD-logic express several major insights diagrams; example, every well-known family A, exhibit formula χA∈LAD an diagram D belongs the A iff χA validated by (when latter viewed as AD-frame). Finally, itself gives rise new interesting diagrams, reflect their profoundly peculiar status.