Related papers: Computational Higher Type Theory II: Dependent Cub…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
We define a naturality construction for the operations of weak omega-categories, as a meta-operation in a dependent type theory. Our construction has a geometrical motivation as a local tensor product with a directed interval, and behaves…
In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the…
Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible…
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
One takes advantage of some basic properties of every homotopic $\lambda$-model (e.g.\ extensional Kan complex) to explore the higher $\beta\eta$-conversions, which would correspond to proofs of equality between terms of a theory of…
This is the second in a series of papers on the relation between algebraic set theory and predicative formal systems. In part I, we introduced the notion of a predicative category of small maps and obtained the result that such categories…
An observable canonical form is formulated for the set of rational systems on a variety each of which is a single-input-single-output, affine in the input, and a minimal realization of its response map. The equivalence relation for the…
In this paper we construct new categorical models for the identity types of Martin-L\"of type theory, in the categories Top of topological spaces and SSet of simplicial sets. We do so building on earlier work of Awodey and Warren, which has…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Dependent types provide a lightweight and modular means to integrate programming and formal program verification. In particular, the types of programs written in dependently typed programming languages (Agda, Idris, F*, etc.) can be used to…
Computational modeling plays an increasingly important role in neuroscience, highlighting the philosophical question of how computational models explain. In the context of neural network models for neuroscience, concerns have been raised…
We present a type theory dealing with non-linear, "ordinary" dependent types (which we will call cartesian) and linear types, where both constructs may depend on terms of the former. In the interplay between these, we find new type formers…
We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…