This paper presents a bijection between combinatorial maps and a class of enriched trees,
corresponding to a class of expression trees in some logical systems (constrained lambda …

We present quantitative analysis of various (syntactic and behavioral) properties of random λ-
terms. Our main results are that asymptotically all the terms are strongly normalizing and that …

We consider propositional formulas built on implication. The size of a formula is the number
of occurrences of variables in it. We assume that two formulas which differ only in the …

Despite λ-calculus is now three quarters of a century old, no formula counting λ-terms has
been proposed yet, and the combinatorics of λ-calculus is considered a hard problem. The …

We investigate quantitative properties of BCI and BCK logics. The first part of the article
compares the number of formulas provable in BCI versus BCK logics. We consider formulas …

Let P_k(f) denote the density of and/or trees defining a boolean function f within the set of
and/or trees with fixed number of variables k. We prove that there exists constant B_f such …

We show various (syntactic and behavioral) properties of random λ-terms. Our main results
are that at least 3/4 of the terms are strongly normalizing and that any fixed closed term …

We consider the logical system of Boolean expressions built on the single connector of
implication and on positive literals. Assuming all expressions of a given size to be equally …

We present a quantitative comparison of classical and intuitionistic logics, based on the
notion of density, within the framework of several propositional languages. In the most …

Since the 1990s, the probability distribution on Boolean functions, induced by some random
formulas built upon the connectives And and Or, has been intensively studied. These …