Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998
Association of Mizar Users
A Theory of Boolean Valued Functions and Quantifiers
with Respect to Partitions

Shunichi Kobayashi

Shinshu University, Nagano

Yatsuka Nakamura

Shinshu University, Nagano
Summary.

In this paper, we define the coordinate of partitions. We also
introduce the universal quantifier and the existential quantifier of
Boolean valued functions with respect to partitions. Some predicate
calculus formulae containing such quantifiers are proved. Such a theory
gives a discussion of semantics to usual predicate logic.
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[3]
[12]
[16]
[15]
[13]
[1]
[7]
[11]
[14]
[2]
[8]
[9]
[6]
[5]
[4]

Preliminaries

Coordinate and Quantifiers
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Received December 21, 1998
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