Hennessy-Milner Properties for (Modal) Bi-intuitionistic Logic

Hennessy-Milner Properties via Topological Compactness

“…In classical modal logic and intuitionistic (nonmodal) logic, our results match well-known Hennessy-Milner results [6, Proposition 2.54], [7,Theorem 21], [34, Corollary 3.9], while for modal (dual-and bi-)intuitionistic logic we have described previously unknown Hennessy-Milner classes. In particular, the current approach generalises the results for (modal) bi-intuitionistic logic that were subject of the predecessor paper of the current paper [27].…”

“…cit., is automatic, and all results follow from Theorem 4.10 below. Similarly, the results from Section 5 of [27] about descriptive and finite Bi-int -models are subsumed by Theorem 5.15, again noting that image compactness subsumes both finiteness and being descriptive. Finally, the treatment of bisimulations for modal and epistemic intuitionistic, and tense bi-intuitionistic logic is new.…”

“…Relation to Predecessor Paper. The current paper is an extension of preliminary results reported in [27]. Conceptually, we identify the core notion of image compactness as the key stepping stone in establishing Hennessy-Milner type theorems.…”

“…If we define the operators →, : Up(X, ≤) × Up(X, ≤) → Up(X, ≤) by The logics Int, Int ∂ , Bi-int are sometimes interpreted over posets (rather than pre-orders), for example in the predecessor paper of this one [27] and in [28]. Here, we choose the more general semantics.…”

Maximality of bi-intuitionistic propositional logic

“…The resulting logic is known as Heyting-Brouwer or Bi-intuitionistic logic. In recent years, the study of this very natural logic has received some degree of attention from different scholars [1,2,13,14,15,21,23,24,25]. Our own work in this field has focused on the semantic study of bi-intuitionistic logic.…”