A zero-one law for random sentences in description logics
Bernard Ycart, Marie-Christine Rousset · Mathematics and Computer Science · 2000
We consider the set of sentences in a decidable fragment of first order logic, restricted to unary and binary predicates, expressed on a finite set of objects. Probability distributions on that set of sentences are defined and studied. For large sets of objects, it is shown that under these distributions, random sentences typically have a very particular form, and that all monotone symmetric properties of these random sentences have a probability close to 0 or 1.