Related papers: Extensible Proof Systems for Infinite-State System…
In this paper we present tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a…
In this paper we present analytic tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give…
We propose a local model-checking proof system for a fragment of CTL. The rules of the proof system are motivated by the well-known fixed-point characterisation of CTL based on unfolding of the temporal operators. To guarantee termination…
Automata operating on infinite objects feature prominently in the theory of the modal $\mu$-calculus. One such application concerns the tableau games introduced by Niwi\'{n}ski & Walukiewicz, of which the winning condition for infinite…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
There have been several recent suggestions for tableau systems for deciding satisfiability in the practically important branching time temporal logic known as CTL*. In this paper we present a streamlined and more traditional tableau…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
In this paper we present a tableau proof system for first order logic of proofs FOLP. We show that the tableau system is sound and complete with respect to Mkrtychev models of FOLP.
In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for…
Fixpoints are an important ingredient in semantics, abstract interpretation and program logics. Their addition to a logic can add considerable expressive power. One general issue is how to define proof systems for such logics. Here we…
We design hypersequent calculus proof systems for the theories of Riesz spaces and modal Riesz spaces and prove the key theorems: soundness, completeness and cut elimination. These are then used to obtain completely syntactic proofs of some…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL+ of the full Alternating time temporal logic ATL*. The method extends…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
In this paper, we focus on discrete-time stochastic systems modelled by nonlinear stochastic difference equations and propose robust abstractions for verifying probabilistic linear temporal specifications. The current literature focuses on…
The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
We prove the syntactic soundness of classical tableaux with free variables and on-the-fly Skolemization. Soundness proofs are usually built from semantic arguments, and this is to our knowledge, the first proof that appeals to syntactic…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…