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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.
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]
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 ...
Categorial grammar posits a close relationship between the syntax and semantic composition, since it typically treats syntactic categories as corresponding to semantic types. Categorial grammars were developed in the 1930s by Kazimierz Ajdukiewicz and in the 1950s by Yehoshua Bar-Hillel and Joachim Lambek .
A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley ( 1965 ) stating that if a first-order theory in a countable language is categorical in some uncountable cardinality , then it is categorical in all uncountable ...
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.
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.
An inner model of a theory is a model that is obtained by taking a substructure of another model. in rebus vagueness The view that vagueness is a feature of the world, rather than of language or of human knowledge. [123] Contrast epistemic vagueness and semantic vagueness. See also ontic vagueness. insolubilia