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827
A Category-theoretic characterization of functional completeness
, 1990
"... . Functional languages are based on the notion of application: programs may be applied to data or programs. By application one may define algebraic functions; and a programming language is functionally complete when any algebraic function f(x 1 ,...,x n ) is representable (i.e. there is a constant a ..."
Abstract
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Cited by 9 (2 self)
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a such that f(x 1 ,...,x n ) = (a . x 1 . ... . x n ). Combinatory Logic is the simplest type-free language which is functionally complete. In a sound category-theoretic framework the constant a above may be considered as an "abstract gödel-number" for f, when gödel
Net Refinement By Pullback Rewriting
- FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES, LECTURE NOTES IN COMPUTER SCIENCE 1378
, 1998
"... The notion of pullback rewriting has been developed recently as a category theoretical framework for vertex replacement in graphs. Here, the technique ..."
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Cited by 1 (1 self)
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The notion of pullback rewriting has been developed recently as a category theoretical framework for vertex replacement in graphs. Here, the technique
The Category-Theoretic Arithmetic of Information
, 2008
"... We highlight the underlying category-theoretic structure of measures of information flow. We present an axiomatic framework in which communication systems are represented as morphisms, and information flow is characterized by its behavior when communication systems are combined. Our framework includ ..."
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We highlight the underlying category-theoretic structure of measures of information flow. We present an axiomatic framework in which communication systems are represented as morphisms, and information flow is characterized by its behavior when communication systems are combined. Our framework
A category-theoretic approach to representation and analysis of inconsistency in graph-based viewpoints
, 2003
"... Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. This may result in inconsistencies between the descriptions provided by stakeholders. Viewpoints-based approaches have been proposed as a way to ma ..."
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Cited by 2 (2 self)
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to manage incomplete and inconsistent models gathered from multiple sources. In this thesis, we propose a category-theoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about
§0. Notations and Conventions §1. Definitions and First Properties
, 2006
"... � � � We develop the theory of Frobenioids, which may be regarded as a category-theoretic abstraction of the theory of coverings and divisors of function fields and number fields. This sort of abstraction is analogous to the role of Galois category-theoretic framework preserves many of the importan ..."
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� � � We develop the theory of Frobenioids, which may be regarded as a category-theoretic abstraction of the theory of coverings and divisors of function fields and number fields. This sort of abstraction is analogous to the role of Galois category-theoretic framework preserves many
Relational Properties of Domains
- Information and Computation
, 1996
"... New tools are presented for reasoning about properties of recursively defined domains. We work within a general, category-theoretic framework for various notions of `relation' on domains and for actions of domain constructors on relations. Freyd's analysis of recursive types in terms of a ..."
Abstract
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Cited by 115 (6 self)
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New tools are presented for reasoning about properties of recursively defined domains. We work within a general, category-theoretic framework for various notions of `relation' on domains and for actions of domain constructors on relations. Freyd's analysis of recursive types in terms of a
Parallel Transport over Path Spaces
"... Abstract. We develop a framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework. Our results connect with and extend ideas developed for higher gauge theories in the framework of 2-conne ..."
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Cited by 5 (4 self)
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Abstract. We develop a framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework. Our results connect with and extend ideas developed for higher gauge theories in the framework of 2
Word-Sense Disambiguation Using Statistical Models of Roget's Categories Trained on Large Corpora
, 1992
"... This paper describes a program that disambiguates English word senses in unrestricted text using statistical models of the major Roget's Thesaurus categories. Roget's categories serve as approximations of conceptual classes. The categories listed for a word in Roget's index tend to ..."
Abstract
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Cited by 345 (14 self)
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to correspond to sense distinctions; thus selecting the most likely category provides a useful level of sense disambiguation. The selection of categories is accomplished by identifying and weighting words that are indicative of each category when seen in context, using a Bayesian theoretical framework. Other
The Geometry of Frobenioids I: The General Theory
, 2006
"... � � � We develop the theory of Frobenioids, which may be regarded as a category-theoretic abstraction of the theory of divisors and line bundles on models of finite separable extensions of a given function field or number field. This sort of abstraction is analogous to the role of Galois categories ..."
Abstract
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Cited by 12 (11 self)
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categories in Galois theory or monoids in the geometry of log schemes. This abstract category-theoretic framework preserves many of the important features of the classical theory of divisors and line bundles on models of finite separable extensions of a function field or number field such as the global
Submitted to: LINEARITY 2014 A Linear/Producer/Consumer Model of Classical Linear Logic
"... This paper defines a new proof- and category-theoretic framework for classical linear logic that sep-arates reasoning into one linear regime and two persistent regimes corresponding to! and?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semant ..."
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This paper defines a new proof- and category-theoretic framework for classical linear logic that sep-arates reasoning into one linear regime and two persistent regimes corresponding to! and?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same
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