Related papers: On the Identity Type as the Type of Computational …

Similarity networks are important abstractions in many information management applications such as recommender systems, corpora analysis, and medical informatics. For instance, by inducing similarity networks between movies rated similarly…

We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…

We study the coherence and conservativity of extensions of dependent type theories by additional strict equalities. By considering notions of congruences and quotients of models of type theory, we reconstruct Hofmann's proof of the…

We propose a computer-algebraic, order-theoretic framework based on intuitionistic logic for the computer-aided discovery of personality axioms from personality-test data and their mathematical categorisation into formal personality…

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured in the identity of the…

This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…

Following a project of developing conventions and notations for informal type theory carried out in the homotopy type theory book for a framework built out of an augmentation of constructive type theory with axioms governing…

Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…

We investigate algebraic and compositional properties of abstract multiway rewriting systems, which are archetypical structures underlying the formalism of the Wolfram model. We demonstrate the existence of higher homotopies in this class…

We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics…

In the literature the empirical characteristic function method is presented as an off-line identification method. While the results of the off-line methods are attractive, the proposed algorithms are ill-conditioned in many cases so that…

Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the "synthetic" development of homotopy…

Categories of paths are a generalization of several kinds of oriented discrete data that have been used to construct $C^*$-algebras. The techniques introduced to study these constructions apply almost verbatim to the more general situation…

System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…

In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and…

Category theory has been recently used as a tool for constructing and modeling an information flow framework. Here, we show that the flow of information can be described using preradicals. We prove that preradicals generalize the notion of…

Some advantages of Cubical Type Theory, as implemented by Cubical Agda, over intensional Martin-L\"of Type Theory include Quotient Inductive Types (QITs), which exist as instances of Higher Inductive Types, and functional extensionality,…

We consider the problem of exact probabilistic inference for Union of Conjunctive Queries (UCQs) on tuple-independent databases. For this problem, two approaches currently coexist. In the extensional method, query evaluation is performed by…

This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…

We describe a type system for a platform called the General Intensional Programming System (GIPSY), designed to support intensional programming languages built upon intensional logic and their imperative counter-parts for the intensional…