Related papers: Affine logic with the integration operator

We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations,…

We prove a factorizable version of the Feigin-Frenkel theorem on the center of the completed enveloping algebra of the affine Kac-Moody algebra attached to a simple Lie algebra at the critical level. On any smooth curve C we consider a…

We focus on a branch of region-based spatial logics dealing with affine geometry. The research on this topic is scarce: only a handful of papers investigate such systems, mostly in the case of the real plane. Our long-term goal is to…

An algebraic proof is presented for the finite strong standard completeness of involutive uninorm logic with fixed point. The result may provide a first step towards settling the open standard completeness problem for involutive uninorm…

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 develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…

We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our…

A theoretical development is carried to establish fundamental results about rank-initial embeddings and automorphisms of countable non-standard models of set theory, with a keen eye for their sets of fixed points. These results are then…

We develop a theory of motives with compact support for logarithmic schemes over a field. Starting from the notion of finite logarithmic correspondences with compact support, we define the logarithmic motive with compact support analogous…

The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…

We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the…

Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…

Given a finite index subfactor, we show that the {\em affine morphisms at zero level} in the affine category over the planar algebra associated to the subfactor is isomorphic to the fusion algebra of the subfactor as a *-algebra. This…

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H. We start with some basic properties of affine embeddings and…

We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…

We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the…

We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…

This paper has two parts. First, we complete the proof of the Kolmogorov extension theorem for unbounded random variables using compactness theorem of integral logic which was proved for bounded case in [8]. Second, we give a proof of the…

For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect…