Minimal propositional calculus
From Encyclopedia of Mathematics
minimal calculus of expressions
The logical calculus obtained from the positive propositional calculus by the addition of a new connective
(negation) and the axiom scheme
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which is called the law of reductio ad absurdum.
The minimal propositional calculus is distinguished by the fact that in it not every formula is deducible from "false" , that is, from a formula of the form . The minimal propositional calculus can be obtained from the calculus
in another way by adding to the language instead of the connective
a new propositional constant
(falsehood) without the addition of new axiom schemes. Here the formula
serves as the negation
of a formula
.
References
[1] | A. Church, "Introduction to mathematical logic" , 1 , Princeton Univ. Press (1956) |
How to Cite This Entry:
Minimal propositional calculus. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Minimal_propositional_calculus&oldid=32858
Minimal propositional calculus. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Minimal_propositional_calculus&oldid=32858
This article was adapted from an original article by S.K. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article