Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

Predicate Calculus for Boolean Valued Functions. Part III


Shunichi Kobayashi
Shinshu University, Nagano
Yatsuka Nakamura
Shinshu University, Nagano

Summary.

In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of Boolean valued functions with respect to partitions. Such a theory is an analogy of usual predicate logic.

MML Identifier: BVFUNC11

The terminology and notation used in this paper have been introduced in the following articles [9] [2] [11] [14] [13] [12] [7] [1] [10] [8] [3] [5] [4] [6]

Contents (PDF format)

  1. Preliminaries
  2. Predicate Calculus

Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[4] Shunichi Kobayashi and Kui Jia. A theory of Boolean valued functions and partitions. Journal of Formalized Mathematics, 10, 1998.
[5] Shunichi Kobayashi and Kui Jia. A theory of partitions. Part I. Journal of Formalized Mathematics, 10, 1998.
[6] Shunichi Kobayashi and Yatsuka Nakamura. A theory of Boolean valued functions and quantifiers with respect to partitions. Journal of Formalized Mathematics, 10, 1998.
[7] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.
[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[10] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[13] Edmund Woronowicz. Interpretation and satisfiability in the first order logic. Journal of Formalized Mathematics, 2, 1990.
[14] Edmund Woronowicz. Many-argument relations. Journal of Formalized Mathematics, 2, 1990.

Received July 14, 1999

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