The proof system G∗ 0 of the quantified propositional calculus corresponds to NC1 , and G∗ 1 corresponds to P, but no formula-based proof system that corresponds log space rea...
Abstract. The paper develops fuzzy attribute logic, i.e. a logic for reasoning about formulas of the form A ⇒ B where A and B are fuzzy sets of attributes. A formula A ⇒ B repr...
Church's Higher Order Logic is a basis for proof assistants -- HOL and PVS. Church's logic has a simple set-theoretic semantics, making it trustworthy and extensible. We ...
Abstract : The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prov...
Set theories are traditionally based on first-order logic. We show that in a constructive setting, basing a set theory on a dependent logic yields many benefits. To this end, we...