General Frames for Relevant Modal Logics

Modal Logics of Reactive Frames

A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the ...

Modal Logics That Need Very Large Frames

The Kuznetsov–Index of a modal logic is the least cardinal μ such that any consistent formula has a Kripke–model of size ≤ μ if it has a Kripke–model at all. The Kuznetsov–Spectrum is the set of all Kuznetsov–Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov–Index iω+ω. Futhermore, Chagrov has constructed an extension...

A General Theorem Prover for Quantified Modal Logics

The main contribution of this work is twofold. It presents a modular tableau calculus, in the free-variable style, treating the main domain variants of quantified modal logic and dealing with languages where rigid and non-rigid designation can coexist. The calculus uses, to this end, light and simple semantical annotations. Such a general proof-system results from the fusion into a unified fram...

A general method for proving decidability of intuitionistic modal logics

We generalise the result of [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34] on decidability of the two variable monadic guarded fragment of first order logic with constraints on the guard relations expressible in monadic second order logic. I...

A General Proof of Kripke-completeness for Quantified Modal Logics