相关论文: Normalization and cut-elimination theorems for som…

This paper presents a sound, complete, and decidable analytic tableau system for the logic of evidence and truth \letf, introduced in Rodrigues, Bueno-Soler \& Carnielli (Synthese, DOI: 10.1007/s11229-020-02571-w, 2020). \letf\ is an…

The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules…

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 explores the connection between two central results in the proof theory of classical logic: Gentzen's cut-elimination for the sequent calculus and Herbrands "fundamental theorem". Starting from Miller's expansion-tree-proofs, a…

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…

This paper introduces the logic $QLET_{F}$, a quantified extension of the logic of evidence and truth $LET_{F}$, together with a corresponding sound and complete first-order non-deterministic valuation semantics. $LET_{F}$ is a…

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…

The four-valued semantics of Belnap--Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several non-classical logics depending on which feature of propositions we wish to preserve: truth, non-falsity,…

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 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.

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 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…

This paper investigates the proof-theoretic foundations of double negation introduction (DNI) and double negation elimination (DNE) in classical logic. By examining both sequent calculus and natural deduction, it is shown that these rules…

In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…

This paper concerns an expansion of first-order Belnap-Dunn logic whose connectives and quantifiers all have a counterpart in classical logic. The language and logical consequence relation of this paradefinite logic are defined, a sequent…

We consider certain infectious logics (Sfde, dSfde, K3w, and PWK) and several their non-infectious modifications, including two new logics, reformulate previously constructed natural deduction systems for them (or present such systems from…

Urban and Bierman introduced a calculus of proof terms for the sequent calculus LK with a strongly normalizing reduction relation. We extend this calculus to simply-typed higher-order logic with inferences for induction and equality, albeit…

The aim of this paper is to introduce the logics FFDE and FN4, which are universally free versions of Belnap-Dunn's four-valued logic, also known as the logic of first-degree entailment (FDE), and Nelson's paraconsistent logic QN4 (N-).…

We extend to natural deduction the approach of Linear Nested Sequents and of 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction -- only one…

In the realm of light logics deriving from linear logic, a number of variants of exponential rules have been investigated. The profusion of such proof systems induces the need for cut-elimination theorems for each logic, the proof of which…