Related papers: Proof nets for Herbrand's Theorem
We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing. In this work we take a coarser (and…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information of which instances…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances…
Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…
Herbrand's theorem is often presented as a corollary of Gentzen's sharpened Hauptsatz for the classical sequent calculus. However, the midsequent gives Herbrand's theorem directly only for formulae in prenex normal form. In the Handbook of…
Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…
Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a…
This paper represents classical propositional proofs as *combinatorial proofs*, which are more abstract than proof nets: superposition (contraction/weakening) is modelled mathematically, as a lax form of fibration, rather than syntactically…
This paper is intended to provide an introduction to cut elimination which is accessible to a broad mathematical audience. Gentzen's cut elimination theorem is not as well known as it deserves to be, and it is tied to a lot of interesting…
We present a sequent calculus for the Grzegorczyk modal logic Grz allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.…
We present a structural representation of the Herbrand content of LK-proofs with cuts of complexity prenex Sigma-2/Pi-2. The representation takes the form of a typed non-deterministic tree grammar of order 2 which generates a finite…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
We show how Leibnitz.s indiscernibility principle and Gentzen's original work lead to extensions of the sequent calculus to first order logic with equality and investigate the cut elimination property. Furthermore we discuss and improve the…
Herbrand's Theorem is a fundamental result in mathematical logic which provides a reduction of first-order formulas satisfied by a universal class to formulas free of existential quantifiers. In this work, a simpler and self-contained…
We give a linear nested sequent calculus for the basic normal tense logic Kt. We show that the calculus enables backwards proof-search, counter-model construction and syntactic cut-elimination. Linear nested sequents thus provide the…
We develop a Gentzen-style proof theory for super-Belnap logics (extensions of the four-valued Dunn-Belnap logic), expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood…
We present a sequent calculus for the modal Grzegorczyk logic Grz allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.
In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N and the logic of first-degree entailment FDE, also known as Belnap-Dunn four-valued…