The permutability equation G(G(x, y), z) = G(G(x, z), y) is satisfied by many scientific and geometric laws. A few examples among many are: The LorentzFitzGerald Contraction, Beer’s Law, the Pythagorean Theorem, and the formula for computing the volume of a cylinder. If we required that a permutable law be meaningful, the possible forms of a law are considerably restricted. The class of example...

We prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleene’s G3) are inter-permutable (using a set of basic “permutation reduction rules” derived from Kleene’s work in 1952) iff they determine the same natural deduction. The basic rules form a confluent and weakly normalising rewriting system. §

We discuss containment checking for regular expressions with operators like XML Schema’s xs:all, that is, the operator that allows a sequence of letters to occur in arbitrary order. In this report, we model this operator by &, and give several algorithms of containment checking for regular expressions with &. Our algorithms are based on the notion of the permutability of word languages. Keyword...

Capitalizing upon Implicit Leadership Theories (ILTs) and Leader-member exchange (LMX), this research aims to explore the relationship between the congruence of employees’ ILTs and those traits of their managers and employees’ supportiveness, resistance and behavioral creativity for change. After distributing three questionnaires at three points among teachers, 296 participants completed all th...