Pratt, V.: Chu spaces from the representational viewpoint. Ann. Pure Appl. Logic 96 no. 1-3, 319--333, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....measurement. As a result, it is not possible to uniquely reconstruct an object from measurement results. In other words, each measurement is a function r(x; y) of two variables: an object x and a (not completely known) measuring device y. Such a function describes a so called Chu space (see, e.g. [1, 2, 7, 8, 20, 21, 22, 23, 24, 25, 26]) 1.3 Precise Definition of a Chu Space To be more precise, to define a Chu space, we must fix a set K (of possible values) Then, a K Chu space is defined as a triple (X; r; Y ) where X and Y are sets, and r : X Theta Y K is a function which maps every 1 pair (x; y) of elements x 2 X and ....

....Y ) is called a morphism of Chu spaces if it satisfies the property (2) for all x 2 X and for all z 2 Y 0 . 1.7 Applications to Parallelism and to Information Flow The notion of Chu spaces was actively used by V. Pratt (Stanford) for describing parallel problem solving algorithms (see, e.g. [7, 8, 20, 21, 22, 23, 24, 25, 26]) and by J. Barwise (Indiana) to describe information flow in general (see, e.g. 3] 2 Fuzzy as a Natural Particular Case of Chu Spaces Before we describe how Chu spaces can be used to justify fuzzy heuristics, let us show that fuzzy methodology can indeed be reformulated in Chu space ....

V. R. Pratt, Chu spaces from the representational viewpoint, Parikh Festschrift, 1997.

....As a result, it is not possible to uniquely reconstruct an object from measurement results. In other words, each measurement is a function r(x; y) of two variables: an object x and a (not completely known) measuring device y. Such a function describes a so called Chu space (see, e.g. [1, 2, 7, 8, 16, 17, 18, 19, 20, 21, 22]) 1.3. Precise definition of a Chu space To be more precise, to define a Chu space, we must fix a set K (of possible values) Then, a K Chu space is defined as a triple (X; r; Y ) where X and Y are sets, and r : X Theta Y K is a function which maps every pair (x; y) of elements x 2 X and y ....

.... Y ) is called a morphism of Chu spaces if it satisfies the property (2) for all x 2 X and for all z 2 Y 0 . 1.7. Applications to parallelism and to information flow The notion of Chu spaces was actively used by V. Pratt (Stanford) for describing parallel problemsolving algorithms (see, e.g. [7, 8, 16, 17, 18, 19, 20, 21, 22]) and by J. Barwise (Indiana) to describe information flow in general (see, e.g. 3] 2. Chu spaces as a uniform justification for fuzzy techniques 2.1. Fuzzy is a particular case of Chu spaces Fuzzy knowledge can be naturally described as a Chu space (X; r; Y ) where X is the set of all ....

V. R. Pratt, Chu spaces from the representational viewpoint, Parikh Festschrift, 1997.

....theorem, simple semigroups are in 1 1 correspondence with functions Y Theta X H . Such functions form the basis of a new approach to foundations of concurrency and foundations of computer science in general which is promoted by V. R. Pratt from Stanford under the name of Chu spaces (see, e. g, [5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]) Thus, a general extension of t norms naturally leads us to Chu spaces. Auxiliary Results and Their Relationship With the Existence and Borderline Character of Classical Truth Values. According to [1] Theorem 1.8, and [11] Theorem 1.4.2, if a compact topological semigroup S is not a group ....

V. R. Pratt, "Chu spaces from the representational viewpoint", Parikh Festschrift, 1997.

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Pratt, V.: Chu spaces from the representational viewpoint. Ann. Pure Appl. Logic 96 no. 1-3, 319--333, 1999.

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V. R. Pratt, Chu spaces from the representational viewpoint, Parikh Festschrift, 1997.

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