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There are multiple definitions of DisCoCat in the literature, depending on the choice made for the compositional aspect of the model. The common denominator between all the existent versions, however, always involves a categorical definition of DisCoCat as a structure-preserving functor from a category of grammar to a category of semantics, which usually encodes the distributional hypothesis.
Among his work mentioned in the laudation are his contributions to domain theory, game semantics, and categorical approach to quantum computation and information. [15] He was elected Fellow of ACM (2014) For contributions to domains in logical form, game semantics, categorical quantum mechanics, and contextual semantics. [1]
Combinatory categorial grammar (CCG) is an efficiently parsable, yet linguistically expressive grammar formalism.It has a transparent interface between surface syntax and underlying semantic representation, including predicate–argument structure, quantification and information structure.
The field of formal semantics encompasses all of the following: The definition of semantic models; The relations between different semantic models; The relations between different approaches to meaning; The relation between computation and the underlying mathematical structures from fields such as logic, set theory, model theory, category ...
Categorical semantics Categorical logic introduces the notion of structure valued in a category C with the classical model theoretic notion of a structure appearing in the particular case where C is the category of sets and functions. This notion has proven useful when the set-theoretic notion of a model lacks generality and/or is inconvenient.
Another appealing aspect of categorial grammars is that it is often easy to assign them a compositional semantics, by first assigning interpretation types to all the basic categories, and then associating all the derived categories with appropriate function types. The interpretation of any constituent is then simply the value of a function at ...
a categorical model of bunched logic is a single category possessing two closed structures, one symmetric monoidal closed the other cartesian closed. A host of categorial models can be given using Day's tensor product construction. [8] Additionally, the implicational fragment of bunched logic has been given a game semantics. [9]
In contrast, predicates s-select the semantic content of their arguments. Thus s-selection is a semantic concept, whereas c-selection is a syntactic one. When the term selection or selectional restrictions appears alone without the c-or s-, s-selection is usually understood. [6] [7]