Related papers: A Labelled Analytic Theorem Proving Environment fo…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Many NLP learning tasks can be decomposed into several distinct sub-tasks, each associated with a partial label. In this paper we focus on a popular class of learning problems, sequence prediction applied to several sentiment analysis…
We use a labelled deduction system based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the…
We present a new Convolutional Neural Network (CNN) model for text classification that jointly exploits labels on documents and their component sentences. Specifically, we consider scenarios in which annotators explicitly mark sentences (or…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
This paper addresses image classification through learning a compact and discriminative dictionary efficiently. Given a structured dictionary with each atom (columns in the dictionary matrix) related to some label, we propose cross-label…
In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the…
Existing technology can parse arbitrary context-free grammars, but only a single, static grammar per input. In order to support more powerful syntax-extension systems, we propose reflective grammars, which can modify their own syntax during…
Standard methods of using categorical variables as predictors either endow them with an ordinal structure or assume they have no structure at all. However, categorical variables often possess structure that is more complicated than a linear…
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 provide an effect system CatEff based on a category-graded extension of algebraic theories that correspond to category-graded monads. CatEff has category-graded operations and handlers. Effects in CatEff are graded by morphisms of the…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…
A well-known approach to treating syntactic island constraints in the setting of Lambek grammars consists in adding specific bracket modalities to the logic. We adapt this approach to abstract categorial grammars (ACG). Thus we define…