Related papers: Modular constructive Lyndon interpolation for nond…

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

We present a formalization of a version of Abadi and Plotkin's logic for parametricity for a polymorphic dual intuitionistic/linear type theory with fixed points, and show, following Plotkin's suggestions, that it can be used to define a…

Using polyadic MV algebras, we show that many predicate many valued logics have the interpolation property.

The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…

In this paper, we present an algorithmic approach to design and construct planar truss structures based on symmetric lattices using modular elements. The method of assembly is similar to Leonardo grids as they both rely on the property of…

We provide a general and syntactically-defined family of sequent calculi, called \emph{semi-analytic}, to formalize the informal notion of a "nice" sequent calculus. We show that any sufficiently strong (multimodal) substructural logic with…

We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…

Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…

Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of tableaux calculi, a refutation approach to display calculi…

We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…

We show that a vast class of finitary fragments of geometric logic admit a form of Craig interpolation property. In doing so, we provide a new dictionary to import technology from algebraic logic to categorical logic.

We present a novel linear $\lambda$-calculus for Classical Multiplicative Exponential Linear Logic (\MELL) along the lines of the propositions-as-types paradigm. Starting from the standard term assignment for Intuitionistic Multiplicative…

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…

The ability to compose code in a modular fashion is important to the construction of large programs. In the logic programming setting, it is desirable that such capabilities be realized through logic-based devices. We describe an approach…

We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…

We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…

This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…