On the Density of Truth of Locally Finite Logics

Z. Kostrzycka
2009 Journal of Logic and Computation  
For the given logical calculus we investigate the size of the fraction of true formulas of a certain length n against the number of all formulas of this length. We are especially interested in asymptotic behaviour of this fraction when n tends to infinity. If the limit of the fraction exists it represents a number which we call the density of truth for the investigated logic. In this paper we apply this approach to the Dummett intermediate linear logic (see [2] ). This paper shows the exact
more » ... ity of this logic and demonstrates that it covers a substantial part of classical propositional calculus. In fact, despite strictly mathematical means used to solve all discussed problems, this paper may have a philosophical impact on understanding to what extent the phenomenon of truth is sporadic or frequent in random mathematics sentences.
doi:10.1093/logcom/exp034 fatcat:6lfuzsau4ne37mn2x3dfm32x4i