Related papers: Labelled tableaux for interpretability logics
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…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…
We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic. The proof system is clausal tableaux, which stems from first-order ATP. Our results are…
We present a new approach to the global fairness verification of tree-based classifiers. Given a tree-based classifier and a set of sensitive features potentially leading to discrimination, our analysis synthesizes sufficient conditions for…
Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s.…
We study multimodal logics over universally first-order definable classes of frames. We show that even for bimodal logics, there are universal Horn formulas that define set of frames such that the satisfiability problem is undecidable, even…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
We set out a general methodology for producing tableau systems for propositional logics via a tableau metatheory that provides general and formal notions for different tableau systems that vary by semantics or formulae. Moreover, by dint of…
This paper revisits soundness and completeness of proof systems for proving that sets of states in infinite-state labeled transition systems satisfy formulas in the modal mu-calculus. Our results rely on novel results in lattice theory,…
This paper presents an end-to-end system for fact extraction and verification using textual and tabular evidence, the performance of which we demonstrate on the FEVEROUS dataset. We experiment with both a multi-task learning paradigm to…
We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Linearisability is a central notion for verifying concurrent libraries: a given library is proven safe if its operational history can be rearranged into a new sequential one which, in addition, satisfies a given specification.…