Related papers: Weak Typed Boehm Theorem on IMLL

We establish new measures of linear independence of logarithms on commutative algebraic groups in the so-called \emph{rational case}. More precisely, let k be a number field and v_{0} be an arbitrary place of k. Let G be a commutative…

We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…

The Omitting Types Theorem in model theory and the Baire Category Theorem in topology are known to be closely linked. We examine the precise relation between these two theorems. Working with a general notion of logic we show that the…

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.…

According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of local…

In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…

In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…

This paper develops a {\em qualitative} and logic-based notion of similarity from the ground up using only elementary concepts of first-order logic centered around the fundamental model-theoretic notion of type.

We study L\"owenheim-Skolem and Omitting Types theorems in Transition Algebra, a logical system obtained by enhancing many sorted first-order logic with features from dynamic logic. The sentences we consider include compositions, unions,…

Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. It turned out that full propositional Linear Logic is undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more expressive than…

We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…

We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an…

We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct manner with little reliance on general coherence results. We…

This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…

In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should…

A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…

An Independent Parallelism Theorem is proven in the theory of adhesive HLR categories. It shows the bijective correspondence between sequential independent and parallel independent direct derivations in the Weak Double-Pushout framework,…

We define weak units in a semi-monoidal 2-category $\CC$ as cancellable pseudo-idempotents: they are pairs $(I,\alpha)$ where $I$ is an object such that tensoring with $I$ from either side constitutes a biequivalence of $\CC$, and $\alpha:…

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…

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the…