Related papers: From 2-sequents and Linear Nested Sequents to Natu…

The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…

In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…

Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…

In this article we present a class of formulas Fn, n in Nat, that need at least 2^n assumptions to be proved in a normal proof in Natural Deduction for purely implicational minimal propositional logic. In purely implicational classical…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…

We present a novel investigation into the consistency operator ($\circ$), traditionally associated with paraconsistent logics, as a means of capturing non-normal modal classicalities within the Kripke framework. By semantically…

The model theory of a first-order logic called N^4 is introduced. N^4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N^4 is very close to classical logic: N^4 has two truth values;…

Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…

Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…

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…

We introduce cut-free nested sequent systems for a broad class of quantified modal logics (QMLs). The QMLs we consider are semantically defined using relational models that assign both an inner and outer domain to each world. This rich…

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke (NAND) and Peirce's…

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…

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…

The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…

Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…

This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de…

The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which…

We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models and, hence, the results apply to a wide class of modal logics including, for example,…