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Summary: How to tell the truth without knowing what you are talking about
George Boole and the Boolean algebra
Luca Anselma, Davide Cavagnino
Dipartimento di Informatica Universitą degli Studi di Torino
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Matthew 5:37
But let your communication be, Yea, yea; Nay,
nay: for whatsoever is more than these cometh
of evil.
Matthew 5:37 (King James version)
Introduction
Is it possible to verify whether a statement is true, even without knowing the subject of the
discussion? More precisely, is it possible to extract secure conclusions from a set of premises
describing what you may not know? The answer is positive provided that the reasoning, from the
accepted set of premises to the conclusions, is correct. The problem of verifying whether a
reasoning is correct is one of the aims of logic since Aristotle. In particular, modern logic, that is
logic since the Renaissance, aims at improving human reasoning and overcoming its fallacies,
significantly by mechanizing reasoning. To this aim, it is necessary to improve logic passing from
the syllogistic doctrine towards more powerful forms of reasoning and to devise a precise logical
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