This talk presents numerous results from the area of quantitative investigations in logic and computability. We present a quantitative analysis of random formulas or random lambda term or finally random combinatory logic terms. Our main goal is to investigate likelihood of semantic properties of random computational objects.<\/p>\n
For the given logical calculus we investigate the proportion of the number of distinguished formulas (or types or terms of a certain calculus) of length n<\/em> to the number of all objects of such length. We are interested in asymptotic behavior of this fraction when length n<\/em> tends to infinity. For the given set A of objects the limit \u0016l(A)<\/em> if exists, is an asymptotic probability of finding formula from the class A<\/em> among all formulas or may also be interpreted as the asymptotic density of the set A<\/em>.<\/p>\n Results obtained are having some philosophical flavor like for example: This talk presents numerous results from the area of quantitative investigations in logic and computability. We present a quantitative analysis of random formulas or random lambda term or finally random combinatory logic terms. Our main goal is to investigate likelihood … Czytaj dalej
\n1. How big is the fraction of one logic being sub-logic of the bigger one based onthe same language?<\/em>
\n2. Estimate the chances that random formula is true or how big is the fraction of tautologies?<\/em>
\n3. What are chances that random program terminates?<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"