Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about well-behaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is c...

We give sound and complete analytic tableau systems for the propositional bimodal logics KB, KB C , KB 5, and KB 5C . These logics have two universal modal operators K and B , where K stands for knowing and B stands for believing. The logic KB is a combination of the modal logic S5 (for K ) and KD45 (for B ) with the interaction axioms I : Kφ → Bφ and C : Bφ → K Bφ. The logics KB C , KB 5, KB 5...

The recently introduced Coalgebraic Predicate Logic (CPL) provides a general first-order syntax together with extra modal-like operators that are interpreted in a coalgebraic setting. The universality of the coalgebraic approach allows us to instantiate the framework to a wide variety of situations, including probabilistic logic, coalition logic or the logic of neighbourhood frames. The last ca...

In this paper I analyze David Kaplan’s essay “Opacity”. In “Opacity” Kaplan attempts to dismiss Quine’s concerns about quantification across intensional (modal and intentional) operators. I argue that Kaplan succeeds in showing that quantification across intensional operators is logically coherent and that quantified modal logic is strictly speaking not committed to essentialism. However, I als...

Typical analysis of Markovian models of processes refers only to the expected utility that can be obtained by the process. On the other hand, modal logic offers a systematic method of characterizing processes by combining various modal operators. A multivalued temporal logic for Markov chains and Markov decision processes has been recently proposed in [1]. Here, we discuss how it can be extende...

We propose a relaxation of Kleene algebra by giving up strictness and right-distributivity of composition. This allows the subsumption of Dijkstra’s computation calculus, Cohen’s omega algebra and von Wright’s demonic refinement algebra. Moreover, by adding domain and codomain operators we can also incorporate modal operators. We show that predicate transformers form lazy Kleene algebras, the d...

Modal Kleene algebras are Kleene algebras enriched by forward and backward box and diamond operators. We formalise the symmetries of these operators as Galois connections, complemetarities and dualities. We study their properties in the associated operator algebras and show that the axioms of relation algebra are theorems at the operator level. Modal Kleene algebras provide a unifying semantics...

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness...

We use imperatives to refute a näıve analysis of update potentials (force-operators attaching to sentences), arguing for a dynamic analysis of imperative force as restrictable, directed, and embeddable. We propose a dynamic, non-modal analysis of conditional imperatives, as a counterpoint to static, modal analyses (e.g., Schwager [16]). Our analysis retains Kratzer’s [8] analysis of if-clauses ...

In this paper we point out that standard PDL-like logics with intersection are useful for reasoning about game structures. In particular, they can express coalitional ability operators known from coalition logic and ATL. An advantage of standard, normal, modal logics is a well understood theoretical foundation and the availability of tools for automated verification and reasoning. We study a mi...