Statistics of intuitionistic versus classical logics

Studia Logica 76 (3):307 - 328 (2004)
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Abstract

For the given logical calculus we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit exists it is represented by a real number between 0 and 1 which we may call the density of truth for the investigated logic. In this paper we apply this approach to the intuitionistic logic of one variable with implication and negation. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of one variable (see [2]). Actually, this paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part (more than 93%) of classical prepositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.

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Citations of this work

Fuzzy logics – quantitatively.Zofia Kostrzycka & Marek Zaionc - 2023 - Journal of Applied Non-Classical Logics 34 (1):97-132.
The density of truth in monadic fragments of some intermediate logics.Zofia Kostrzycka - 2007 - Journal of Logic, Language and Information 16 (3):283-302.

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References found in this work

A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.

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