We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an action-based temporal logic in which one can explicitly talk about steps. The logic is studied to establish a variety of positive and negative results in terms of axiomatizability and decidability. Our positive results show that the step notion is amenable to logical treatment via standard techniques. They also help us to obtain a logical characterization of two well known models for distributed systems: labelled elementary net systems and labelled prime event structures. Our negative results show that demanding deterministic structures when dealing with a "noninterleaved " notion of transitions is, from a logical standpoint, very expressive. They also show that another well known model of distributed systems called asynchronous transition systems exhibits a surprising a...

We introduce CoCasl as a simple coalgebraic extension of the algebraic specification language Casl. CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types. We show that the well-known coalgebraic modal logic can be expressed in CoCasl. We present sufficient criteria for the existence of cofree models, also for several variants of nested cofree and free specifications. Moreover, we describe an extension of the existing proof support for Casl (in the shape of an encoding into higher-order logic) to CoCasl.

We provide an elementary proof of the xpoint alternation hierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mu-calculus alternation hierarchy.

This paper presents a work in progress on enhanced Propositional Dynamic Logics for reasoning about actions. Propositional Dynamic Logics (PDL's) are modal logics for describing and reasoning about system dynamics in terms of properties of states and actions

We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequent-based proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satisfy assertions in Hennessy-Milner logic. The main novelty lies in the use of the operational semantics to derive introduction rules, on the left and right of sequents, for the operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semantics specified in the GSOS format. Using a general algebraic notion of GSOS model, we prove a completeness theorem for the cut-free fragment of the proof system, thereby establishing the admissibility of the cut rule. Under mild (and necessary) conditions on the process algebra, an ω-completeness result, relative to the “intended” model of closed process terms, follows.

Abstract. Safety is increasingly important for software based, critical systems. Fault tree analysis (FTA) is a safety technique from engineering, developed for analyzing and assessing system safety by uncovering safety flaws and weaknesses of the system. The main drawback of this analysis technique is, that it is based on informal grounds, so safety flaws may be overlooked. This is an issue, where formal proofs can help. They are a safety techniques from software engineering, which are based on precise system descriptions and allow to prove consistency and other (safety) properties. We present an approach which automatically proves the consistency of fault trees based on a formal model by model checking. Therefore, we define consistency conditions in Computational Tree Logic, a widely used input language for model checkers. In the second part, we exemplify our approach with a case study from the Fault Tree Handbook.

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We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a self-dual logic; constructible duality. We develop a self-dual model by considering an interval of worlds in an intuitionistic Kripke model. The duality arises through how we judge truth and falsity. Truth is judged forward in the Kripke model, as in intuitionistic logic, while falsity is judged backwards, that is forward in the dual model. We define a symmetrization of the Beth-Fitting construction which transforms an interval Kripke model in a self-dual algebra for the logic of constructible duality and back. We then show that every point in the algebra is representable by some formula in the logic. This algebra arises as an instantiation of a pseudo-Boolean algebra into several categorical constructions. In particular, we show that this algebra is an instantiation of the Chu construction applied to a pseudo-Boolea...

We provide decomposition and quotienting results for multi-modal logic with respect to a composition operator, traditionally used for epistemic models, due to van Eijck et al. (Journal of Applied Non-Classical 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 S5 n models, our results apply to the composition of any pair of Kripke models. In particular, our quotienting result extends a specific result in the above mentioned paper by van Eijck et al. for the composition of epistemic models with disjoint sets of atomic propositions to compositions of any two Kripke models regardless of their sets of atomic propositions. We also explore the complexity of the formulas we construct in our decomposition result. Luca Aceto and Anna Ingólfsdóttir were partially supported by the project ‘Processes