Related papers: Tableaux for multi-modal hybrid logic with binders…
Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its…
In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new \emph{binary} sequent calculi (each sequent is a pair of formulae) for…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
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…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
We prove that the sequent calculus $\mathsf{L_{RBL}}$ for residuated basic logic $\mathsf{RBL}$ has strong finite model property, and that intuitionistic logic can be embedded into basic propositional logic $\mathsf{BPL}$. Thus…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
The paper reports on first preliminary results and insights gained in a project aiming at implementing the fluent calculus using methods and techniques based on binary decision diagrams. After reporting on an initial experiment showing…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…
Binary multirelations can model alternating nondeterminism, for instance, in games or nondeterministically evolving systems interacting with an environment. Such systems can show partial or total functional behaviour at both levels of…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
Transition systems are often used to describe the behaviour of software systems. If viewed as a graph then, at their most basic level, vertices correspond to the states of a program and each edge represents a transition between states via…
Metric Temporal Logic $\mathsf{MTL}[\until_I,\since_I]$ is one of the most studied real time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of…