...f those numbers. The main tools we use for dealing with asymptotics of sequences of numbers are known in combinatorics as generating functions. A nice exposition of the method can be found in [4] and =-=[1]-=-. Also see papers [5, 6, 2, 3] for the presentation of this method in logics. Definition 1. We associate the density µ(A) with a subset A of formulas as: if the appropriate limit exists. #{t ∈ A : �t�...

...obability that a randomly chosen implicational formula admits p premises. Question 2: What is a probability that a randomly chosen implicational simple tautology admits p premises.s133 Lemma 16. (see =-=[3]-=-) The asymptotic density of the set of all formulas with p premisses F → k (p) exists and is: µ(F → k (p)) = p 2 p+1. Theorem 17. The random variable X has the following distribution (see Definition 3...

...main tools we use for dealing with asymptotics of sequences of numbers are known in combinatorics as generating functions. A nice exposition of the method can be found in [4] and [1]. Also see papers =-=[5, 6, 2, 3]-=- for the presentation of this method in logics. Definition 1. We associate the density µ(A) with a subset A of formulas as: if the appropriate limit exists. #{t ∈ A : �t� = n} µ(A) = lim n→∞ #{t ∈ F :...

...main tools we use for dealing with asymptotics of sequences of numbers are known in combinatorics as generating functions. A nice exposition of the method can be found in [4] and [1]. Also see papers =-=[5, 6, 2, 3]-=- for the presentation of this method in logics. Definition 1. We associate the density µ(A) with a subset A of formulas as: if the appropriate limit exists. #{t ∈ A : �t� = n} µ(A) = lim n→∞ #{t ∈ F :...