Ordinary Kripke models are not reactive. When we evaluate (test/measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This paper studies Kripke models which react to the evaluation process and change themselves during the process. This is reminiscent of game theoretic semantics where the two sides react to each other...

We study a propositional bimodal logic consisting of two S4 modalities and [a], together with the interaction axiom scheme 〈a〉 φ → 〈a〉φ. In the intended semantics, the plain is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation Ra. The interaction axiom ex...

We provide decomposition and quotienting results for multimodal logic with respect to a composition operator, traditionally used for epistemic models, due to van Eijck et al. (Journal of Applied NonClassical Logics 21(3–4):397–425, 2011), that involves sets of atomic propositions and valuation functions from Kripke models. While the composition operator was originally defined only for epistemic...

abstract. We study a propositional bimodal logic consisting of two S4 modalities £ and [a], together with the interaction axiom scheme a£ϕ → £aϕ. In the intended semantics, the plain £ is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation Ra. The interacti...

Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete characterisation for the expressive power of modal inclusion logic: a class of Kripke models with teams is definable in modal inclusion logic if and only if it is clos...

Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a ...

Resource bisimilarity has been proposed in the literature on concurrency theory as a notion of bisimilarity over labelled transition systems that takes into account the number of choices that a system has. Independently, g-bisimilarity has been defined over Kripke models as a suitable notion of bisimilarity for graded modal logic. This note shows that these two notions of bisimilarity coincide ...

The finite model property of the variety of S-algebras was proved by X. Caicedo using Kripke model techniques of the associated calculus. A more algebraic proof, but still strongly based on Kripke model ideas, was given by Muravitskii. In this article we give a purely algebraic proof for the finite model property which is strongly based on the fact that for every element x in a S-algebra the in...

We present an authorization logic that is quite similar to constructive modal S4. The logic assumes that principals are conceited in their beliefs. We describe the sequent calculus, Hilbert-style axiomatization, and Kripke semantics of the logic. A distinguishing characteristic of the sequent calculus is that hypothetical reasoning is relativized to beliefs of principals. We prove several meta-...