The one variable implicational calculus.

One Variable Advanced Calculus

Single Axioms in the Implicational Propositional Calculus

A class of challenge problems derived from a first-order encoding of the implicational propositional calculus is presented.

Cut-elimination for the mu-calculus with one variable

We establish syntactic cut-elimination for the one-variable fragment of the modal mu-calculus. Our method is based on a recent cut-elimination technique by Mints that makes use of Buchholz' Ω-rule.

Complexity Results of Subclasses of the Pure Implicational Calculus

About 50 years ago Lukasiewicz, Tarski, see 6, 4] and others studied the implicational calculus, i. e. the set PIF (pure implicational formulas) of those propositional formulas that are constructed exclusively from Boolean variables and the propositional implication ! as the only connective. Obviously this class of formulas is not able to represent all Boolean functions. While every formula in ...

Domain Theory and Differential Calculus (Functions of one Variable)

We introduce a domain-theoretic framework for differential calculus. We define the set of primitive maps as well as the derivative of an interval-valued Scott continuous function on the domain of intervals, and show that they are dually related, providing an extension of the classical duality of differentiation and integration as in the fundamental theorem of calculus. It is shown that, for loc...