Related papers: Cut-Simulation and Impredicativity

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the {\pi}-calculus closely related to linear logic. Decompositions of intuitionistic…

The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…

It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…

Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then we present a…

In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, exhibiting a classical…

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A…

We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…

This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in…

This paper studies a first-order expansion of a combination C+J of intuitionistic and classical propositional logic, which was studied by Humberstone (1979) and del Cerro and Herzig (1996), from a proof-theoretic viewpoint. While C+J has…

We introduce and develop propositional continuous intuitionistic logic and propositional continuous affine logic via complete algebraic semantics. Our approach centres on AC-algebras, which are algebras $USC(\mathcal{L})$ of sup-preserving…

We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…

Input/Output (I/O) logic is a general framework for reasoning about conditional norms and/or causal relations. We streamline Bochman's causal I/O logics via proof-search-oriented sequent calculi. Our calculi establish a natural syntactic…

In this paper we present a constructive proof of cut elimination for a system of full second order logic with the structural rules absorbed and using sets instead of sequences. The standard problem of the cutrank growth is avoided by using…

We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…

In our previous work, we proposed the logic obtained from full non-associative Lambek calculus by adding a sort of linear-logical modality. We call this logic non-associative non-commutative intuitionistic linear logic ($\mathbf{NACILL}$,…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the…

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.