Related papers: Constructive validity of a generalized Kreisel-Put…

We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…

Dispersive sum rules constitute long-standing tools for extracting hadron features from QCD. We estimate the systematic uncertainties induced by assuming quark-hadron duality and improve the accuracy of the resulting predictions by…

The starting point of this work is the observation that the Curry-Howard isomorphism, relating types and propositions, programs and proofs, composition and cut, extends to the correspondence of program fusion and cut elimination. This…

Intuitionistic first-order logic extended with a restricted form of Markov's principle is constructive and admits a Curry-Howard correspondence, as shown by Herbelin. We provide a simpler proof of that result and then we study…

Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the…

In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies…

We propose a method to adapt functional logic programming to deal with reasoning on coinductively interpreted programs as well as on inductively interpreted programs. In order to do so, we consider a class of objects interesting for this…

In the general context of computable metric spaces and computable measures we prove a kind of constructive Borel-Cantelli lemma: given a sequence (constructive in some way) of sets $A_{i}$ with effectively summable measures, there are…

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

Propositional G\"odel logic extends intuitionistic logic with the non-constructive principle of linearity $A\rightarrow B\ \lor\ B\rightarrow A$. We introduce a Curry-Howard correspondence for this logic and show that a particularly simple…

The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…

We present a variant of the calculus of deductive systems developed in (Lambek 1972, 1974), and give a generalization of the Curry-Howard-Lambek theorem giving an equivalence between the category of typed lambda-calculi and the category of…

We reprove the countable splitting lemma by adapting Nawrotzki's algorithm which produces a sequence that converges to a solution. Our algorithm combines Nawrotzki's approach with taking finite cuts. It is constructive in the sense that…

Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of…

In his constructive development of complex analysis, Errett Bishop used restrictive notions of homotopy and simple connectedness. Working in Bishop-style constructive mathematics, we prove Cauchy's integral theorem using the standard…

In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell…

Conformal prediction, and split conformal prediction as a specific implementation, offer a distribution-free approach to estimating prediction intervals with statistical guarantees. Recent work has shown that split conformal prediction can…

Split conformal prediction (CP) is arguably the most popular CP method for uncertainty quantification, enjoying both academic interest and widespread deployment. However, the original theoretical analysis of split CP makes the crucial…

After learning basic quantum computing concepts, it is desirable to reinforce the learning using an important and relatively complex algorithm through which the students can observe and appreciate how the qubits evolve and interact with…

Hybrid Answer Set Programming (Hybrid ASP) is an extension of Answer Set Programming (ASP) that allows ASP-like rules to interact with outside sources. The Splitting Set Theorem is an important and extensively used result for ASP. The paper…