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

Contents (PDF format)

1. Preliminaries
2. Coordinate and Quantifiers

Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[2] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[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] Adam Naumowicz and Mariusz Lapinski. On \tone\ reflex of topological space. 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] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.

[10] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[11] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.

[12] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[13] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[14] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

[15] Edmund Woronowicz. Interpretation and satisfiability in the first order logic. Journal of Formalized Mathematics, 2, 1990.

[16] Edmund Woronowicz. Many-argument relations. Journal of Formalized Mathematics, 2, 1990.