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.

#### MML Identifier: BVFUNC_2

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]

#### Contents (PDF format)

1. Preliminaries
2. Coordinate and Quantifiers

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