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The POPLMARK Challenge comprises a set of problems intended to measure the strength of reasoning systems in the realm of mechanizing programming language meta-theory at the time the challenge was enunciated. Included in the collection is…
Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
The Unified Modeling Language (UML) is rapidly emerging as a de-facto standard for modelling OO systems. Given this role, it is imperative that the UML needs a well-defined, fully explored semantics. Such semantics is required in order to…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok-Esakia…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
We introduce a modal logic FIL for Feferman interpretability. In this logic both the provability modality and the interpretability modality can come with a label. This label indicates that in the arithmetical interpretation the axiom set of…
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…
We present a new asynchronous model of computation named Stellar Resolution based on first-order unification. This model of computation is obtained as a formalisation of Girard's transcendental syntax programme, sketched in a series of…
We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of…
In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog that consists of the language LO enriched with the constant 1. We use constraints…
The Minkowski Question Mark function relates the continued-fraction representation of the real numbers, to their binary expansion. This function is peculiar in many ways; one is that its derivative is 'singular'. One can show by classical…
Cyclic proof systems for Heyting and Peano arithmetic eschew induction axioms by accepting proofs which are finite graphs rather than trees. Proving that such a cyclic proof system coincides with its more conventional variants is often…
We use the connection between automata and logic to prove that a wide class of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first we generalize one of the central results in coalgebraic automata theory, namely…
Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic…
Abstract argumentation frameworks are formal systems that facilitate obtaining conclusions from non-monotonic knowledge systems. Within such a system, an argumentation semantics is defined as a set of arguments with some desired qualities,…
In recent work, Chaumont et al. [9] showed that is possible to condition a stable process with index ${\alpha} \in (1,2)$ to avoid the origin. Specifically, they describe a new Markov process which is the Doob h-transform of a stable…