Related papers: Coordination in Categorical Compositional Distribu…
We give a natural-deduction-style type theory for symmetric monoidal categories whose judgmental structure directly represents morphisms with tensor products in their codomain as well as their domain. The syntax is inspired by Sweedler…
Traditional semantic parsers map language onto compositional, executable queries in a fixed schema. This mapping allows them to effectively leverage the information contained in large, formal knowledge bases (KBs, e.g., Freebase) to answer…
An important property of programming language semantics is that they should be compositional. However, unstructured low-level code contains goto-like commands making it hard to define a semantics that is compositional. In this paper, we…
We discuss an extension of the standard logical rules (functional application and abstraction) in Categorial Grammar (CG), in order to deal with some specific cases of polysemy. We borrow from Generative Lexicon theory which proposes the…
We study the compactness of composition operators on the Bergman spaces of certain bounded pseudoconvex domains in $\mathbb{C}^n$ with non-trivial analytic disks contained in the boundary. As a consequence we characterize that compactness…
Different from previous surveys in semantic parsing (Kamath and Das, 2018) and knowledge base question answering(KBQA)(Chakraborty et al., 2019; Zhu et al., 2019; Hoffner et al., 2017) we try to takes a different perspective on the study of…
While there have been extensive studies regarding the theory of composition operators in standard Bergman spaces, there have not been many results pertaining to large Bergman spaces due to a lack of useful tools. In this paper, we give the…
According to the distributional inclusion hypothesis, entailment between words can be measured via the feature inclusions of their distributional vectors. In recent work, we showed how this hypothesis can be extended from words to phrases…
Lexical Semantics is concerned with how words encode mental representations of the world, i.e., concepts . We call this type of concepts, classification concepts . In this paper, we focus on Visual Semantics , namely on how humans build…
Distributional word representation methods exploit word co-occurrences to build compact vector encodings of words. While these representations enjoy widespread use in modern natural language processing, it is unclear whether they accurately…
We study composition operators whose symbols are suitable perturbations of the identity and which act between different weighted modulation classes. We consider both modulation spaces formed by tempered distributions and those whose…
We study a categorical condition on relations, which is a categorical formulation of J\'onsson's characterisation of congruence distributive varieties. Categories satisfying these conditions need not be varieties; for instance, the dual of…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
The focus of the papers presented in this volume is on the interplay between syntax and semantics in case of languages, namely the central question of what a program means and how it does define the intended procedure. This is a crucial…
Words (phrases or symbols) play a key role in human life. Word (phrase or symbol) representation is the fundamental problem for knowledge representation and understanding. A word (phrase or symbol) usually represents a name of a category.…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
The categorical distribution is a natural representation of uncertainty in multi-class segmentations. In the two-class case the categorical distribution reduces to the Bernoulli distribution, for which grayscale morphology provides a range…