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Graded Entailment for Compositional Distributional Semantics
TLDR
The main theorem shows that entailment strength lifts compositionally to the sentence level, giving a lower bound on sentence entailment. Expand
Interacting Conceptual Spaces I : Grammatical Composition of Concepts
TLDR
This work introduces the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications, and shows how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Expand
Interacting Conceptual Spaces
TLDR
This work introduces the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications, and shows how conceptual spaces for composite types such as adjectives and verbs can be constructed. Expand
Custom Hypergraph Categories via Generalized Relations
TLDR
This work presents a conceptually motivated parameterized framework for the construction of models for process theories that generalizes the notion of binary relation along four axes of variation, the truth values, a choice of algebraic structure, the ambient mathematical universe and the choice of proof relevance or provability. Expand
Graded hyponymy for compositional distributional semantics
TLDR
This work exploits the freedom in the abstract categorical framework to change the choice of semantic model, and describes hyponymy as a graded order on meanings, using models of partial information used in quantum computation. Expand
No-Go Theorems for Distributive Laws
  • M. Zwart, Dan Marsden
  • Computer Science, Mathematics
  • 34th Annual ACM/IEEE Symposium on Logic in…
  • 1 June 2019
TLDR
Two families of theorems for showing when there can be no distributive law for two monads are presented, widely generalizing a counterexample attributed to Plotkin and encompassing various new practical situations. Expand
Equational reasoning with lollipops, forks, cups, caps, snakes, and speedometers
TLDR
This paper advocates the use of string diagrams, a two-dimensional form of notation which silently deals with distracting bookkeeping steps in elementary category theory and shows that string diagrams can also easily accommodate objects and arrows. Expand
Generalized Relations in Linguistics and Cognition
Categorical compositional models of natural language exploit grammatical structure to calculate the meaning of sentences from the meanings of individual words. This approach outperforms conventionalExpand
Generalized relations in linguistics & cognition
Categorical compositional models of natural language exploit grammatical structure to calculate the meaning of sentences from the meanings of individual words. This approach outperforms conventionalExpand
Towards Compositional Distributional Discourse Analysis
TLDR
A notion of basic anaphoric discourses is introduced as a mid-level representation between natural language discourse formalised in terms of basic discourse representation structures (DRS); and knowledge base queries over the Semantic Web as described by basic graph patterns in the Resource Description Framework (RDF). Expand
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