Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

## Calculus of Propositions

Jan Popiolek
Warsaw University, Bialystok
Supported by RPBP.III-24.C8.
Andrzej Trybulec
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

### Summary.

Continues the analysis of classical language of first order (see [6], [1], [3], [4], [2]). Three connectives: truth, negation and conjuction are primary (see [6]). The others (alternative, implication and equivalence) are defined with respect to them (see [1]). We prove some important tautologies of the calculus of propositions. Most of them are given as the axioms of classical logical calculus (see [5]). In the last part of our article we give some basic rules of inference.

#### MML Identifier: PROCAL_1

The terminology and notation used in this paper have been introduced in the following articles [7] [3] [4]

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek. Connectives and subformulae of the first order language. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek, Agata Darmochwal, and Andrzej Trybulec. Propositional calculus. Journal of Formalized Mathematics, 2, 1990.
[3] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[4] Agata Darmochwal. A first-order predicate calculus. Journal of Formalized Mathematics, 2, 1990.
[5] Andrzej Grzegorczyk. \em Zarys logiki matematycznej. PWN, Warsaw, 1973.
[6] Piotr Rudnicki and Andrzej Trybulec. A first order language. Journal of Formalized Mathematics, 1, 1989.
[7] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.