We briefly examine the modal formulae that can be derived in Multiplicative Additive Linear Logic (MALL) and some extensions by using Tarksi’s extensional modal operators. We also breifly compare this with a substructural form of the modal logic K.

This paper studies finitary modal logics as specification languages for Set-coalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Set-coalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence. Stone-coalgebras (coalgebras over the category of Stone spaces), on the ot...

Taking Löb’s Axiom in modal provability logic as a running thread, we discuss some general methods for extending modal frame correspondences, mainly by adding fixed-point operators to modal languages as well as their correspondence languages. Our suggestions are backed up by some new results — while we also refer to relevant work by earlier authors. But our main aim is advertizing the perspecti...

Explicit modal logics contain modal-like terms that label formulas in a way that mimics deduction in the system. These logics have certain proof-theoretic advantages over the usual modal logics, perhaps the most important of which is conventional cut-elimination. The present paper studies tableau proof systems for two explicit modal logics, LP and S4LP. Using a certain method to prove the corre...

We investigate a modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action. We focus on the evolution of belief, and propose an integra...

Modal verbs have different interpretations depending on their context. Previous approaches to modal sense classification achieve relatively high performance using shallow lexical and syntactic features. In this work we uncover the difficulty of particular modal sense distinctions by eliminating both distributional bias and sparsity of existing small-scale annotated corpora used in prior work. W...