Related papers: A Fibrational Perspective on Differential Linear L…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…
What is ergonomic syntax for relations? In this first paper in a series of two, to answer the question we define regular calculi: a suitably structured functor from a category representing the syntax of regular logic to the category of…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation,…
The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
We construct a zig-zag of Quillen adjunctions between the homotopy theories of differential graded and simplicial categories. In an intermediate step we generalize Shipley-Schwede's work on connective DG algebras by extending the Dold-Kan…
We address classification of distributional data, where units are described by histogram or interval-valued variables. The proposed approach uses a linear discriminant function where distributions or intervals are represented by quantile…
Liouvillian systems were initially introduced within the framework of differential algebra. They can be seen as a natural extension of differential flat systems. Many physical non flat systems seem to be Liouvillian. We present in this…
The differential representation is a novel formalism for studying boundary correlators in $(d+1)$-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.
We design a library for binary field arithmetic and we supply a core API which is completely developed in DLAL, extended with a fix point formula. Since DLAL is a restriction of linear logic where only functional programs with polynomial…
Signal temporal logic (STL) was introduced for monitoring temporal properties of continuous-time signals for continuous and hybrid systems. Differential dynamic logic (dL) was introduced to reason about the end states of a hybrid program.…
We use a specific implementation of discrete differential geometry to describe Dirac-Kahler fermions in such a way that we can separate their chiral and flavour components. The formulation introduces additional lattices so that on each…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
The straightening-unstraightening correspondence of Grothendieck--Lurie provides an equivalence between cocartesian fibrations between $(\infty, 1)$-categories and diagrams of $(\infty, 1)$-categories. We provide an alternative proof of…