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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.
The first higher-dimensional models of intensional type theory were constructed by Steve Awodey and his student Michael Warren in 2005 using Quillen model categories.These results were first presented in public at the conference FMCS 2006 [5] at which Warren gave a talk titled "Homotopy models of intensional type theory", which also served as his thesis prospectus (the dissertation committee ...
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 ...
"A Fully Abstract Game Semantics for General References" (1998). The award was presented at LiCS 2018. Samson Abramsky and Bob Coecke. "A categorical semantics of quantum protocols." (2004). The award was presented at LiCS 2024. [18] He was awarded an EPSRC Senior Research Fellowship on Foundational Structures and Methods for Quantum ...
For this reason, it is used throughout mathematics. Applications to mathematical logic and semantics (categorical abstract machine) came later. Certain categories called topoi (singular topos) can even serve as an alternative to axiomatic set theory as a foundation of mathematics. A topos can also be considered as a specific type of category ...
The relationship of "Semantic data models" with "physical data stores" and "real world". [1] A semantic data model (SDM) is a high-level semantics-based database description and structuring formalism (database model) for databases. This database model is designed to capture more of the meaning of an application environment than is possible with ...
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 ...
The cognitive approach consists of two concepts: information processing depends on internal representations, and that mental representations undergo transformations.For the first concept, we could describe an object in a number of ways, with drawings, equations, or verbal descriptions, but it is up to the recipient to have a background understanding of the context to which the object is being ...