Morphisms on Bi-approximation Semantics.
Tomoyuki Suzuki · 2012
In the present paper, we introduce bounded morphisms on bi-approximation semantics, show the so-called p-morphism lemma on bi-approximation semantics, and investigate the dual representation of the morphisms. In addition, we study three properties, namely B-embedding, B-separating and B-reflecting, to preserve validity of sequents on frames. These bounded morphisms do not look like embedding, surjective and isomorphic p-morphisms on Kripke semantics in modal logic. Nevertheless, with help of auxiliary relations or properties held via the dual representation, we notice that the notion of our bounded morphisms on bi-approximation semantics is a natural generalisation of the one on Kripke semantics in modal logic.