Related papers: Categorical Vector Space Semantics for Lambek Calc…
This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
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…
In previous work with J. Hedges, we formalised a generalised quantifiers theory of natural language in categorical compositional distributional semantics with the help of bialgebras. In this paper, we show how quantifier scope ambiguity can…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
Distributional semantics creates vector-space representations that capture many forms of semantic similarity, but their relation to semantic entailment has been less clear. We propose a vector-space model which provides a formal foundation…
Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrzadeh and Clark provides a conceptually motivated procedure…
Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional (DisCoCat) model of meaning of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) combines aspected of both to…
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…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
Vector space models have become popular in distributional semantics, despite the challenges they face in capturing various semantic phenomena. We propose a novel probabilistic framework which draws on both formal semantics and recent…
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…
The interpretation of the lexical aspect of verbs in English plays a crucial role for recognizing textual entailment and learning discourse-level inferences. We show that two elementary dimensions of aspectual class, states vs. events, and…
This paper presents the use of probabilistic class-based lexica for disambiguation in target-word selection. Our method employs minimal but precise contextual information for disambiguation. That is, only information provided by the…
The categorical compositional distributional model of Coecke, Sadrzadeh and Clark provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
Categorical compositional distributional semantics (CCDS) allows one to compute the meaning of phrases and sentences from the meaning of their constituent words. A type-structure carried over from the traditional categorial model of grammar…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
We investigate notions of ambiguity and partial information in categorical distributional models of natural language. Probabilistic ambiguity has previously been studied using Selinger's CPM construction. This construction works well for…
Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the "gros" semantics in the category of lcc categories: Instead of constructing an interpretation in a…