Related papers: Fast Cut-Elimination using Proof Terms: An Empiric…

The aim of this work is to characterize three fundamental normalization proprieties in lambda-calculus trough the Taylor expansion of $ \lambda$-terms. The general proof strategy consists in stating the dependence of ordinary reduction…

This paper presents a cut-elimination proof for the logic $LG^\omega$, which is an extension of a proof system for encoding generic judgments, the logic $\FOLDNb$ of Miller and Tiu, with an induction principle. The logic $LG^\omega$, just…

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…

This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…

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 use the combination of argumentative zoning [1] and a legal argumentative scheme to create legal argumentative segments. Based on the argumentative segmentation, we propose a novel task of classifying argumentative segments of legal case…

We introduce a proper display calculus for first-order logic, of which we prove soundness, completeness, conservativity, subformula property and cut elimination via a Belnap-style metatheorem. All inference rules are closed under uniform…

Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…

The framework of cyclic proof systems provides a reasonable proof system for logics with inductive definitions. It also offers an effective automated proof search procedure for such logics without finding induction hypotheses. Recent…

In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic…

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction.

Public announcement logic(PAL) is an extension of epistemic logic (EL) with some reduction axioms. In this paper, we propose a cut-free labelled sequent calculus for PAL, which is an extension of that for EL with sequent rules adapted from…

I give a proof of the confluence of combinatory strong reduction that does not use the one of lambda-calculus. I also give simple and direct proofs of a standardization theorem for this reduction and the strong normalization of simply typed…

We give an improved branch-and-bound solver for the multiterminal cut problem, based on the recent work of Henzinger et al.. We contribute new, highly effective data reduction rules to transform the graph into a smaller equivalent instance.…

Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…

We present the new version of the Loop Acceleration Tool (LoAT), a powerful tool for proving non-termination and worst-case lower bounds for programs operating on integers. It is based on a novel calculus for loop acceleration, i.e.,…

We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…

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…

The paper compares two generic techniques for deriving lower bounds and impossibility results in distributed computing. First, we prove a speedup theorem (a-la Brandt, 2019), for wait-free colorless algorithms, aiming at capturing the…

Je\v{r}\'abek showed that cuts in classical propositional logic proofs in deep inference can be eliminated in quasipolynomial time. The proof is indirect and it relies on a result of Atserias, Galesi and Pudl\'ak about monotone sequent…