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Gödel also proved that no logical system for mathematics could, by its own devices, be shown to be free from inconsistency, a result known as the second incompleteness theorem.
Beginning with a logical system for mathematics, one presumed to be free of contradictions, he invented an ingenious scheme that allowed the formulas in it to engage in a sort of double speak.
A logical system for a language is a set of axioms and rules designed to prove exactly the valid arguments statable in the language.
At the time when Gentzen worked out his system of natural deduction, Stanislaw Jaskowski was also developing a logical system for reasoning with assumptions.
The new geometry posed a radical challenge to Euclidean geometry, because it denied traditional geometry its best claim to certainty, to wit, that it was the only logical system for discussing geometry at all.
Open access advocates say that's not only a more logical system for research funded by the public, but a much better way of disseminating scientific discovery.
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Halpern then considers the formal logical systems for reasoning about uncertainty.
This paper considers the logical system of Josiah Royce as a development of the idealist version and argues that it has the potential to account both for modern logical systems and for the place of agency and purpose in logic.
He was trained at Athens in the eclectic New Academy, and eclectic he apparently remained, seeking a philosophy to fit his own constitution rather than a logical system valid for all.
This article is about a breadth-first exploration of logical concepts in cryptography and their linguistic abstraction and model-theoretic combination in a comprehensive logical system, called CPL (for Cryptographic Protocol Logic).
In (Nogina 2006, Nogina 2007) a complete logical system, \(\mathsf{GLA}\), for proofs and provability was offered, in the sum of the original languages of \(\mathsf{GL}\) and \(\mathsf{LP}\).
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