Common use of Properties of homogeneous relations Clause in Contracts

Properties of homogeneous relations. As argued in section 2.2.1.5, precedence is a homogeneous relation. The other axiom of precedence is connectedness, defined below. A relation R is connected if each pair of elements in the domain of R is joined by a sequence of pairs in R. (xxii) The axiom is quite inconsequential for φ-Correspondence, but notice that like totality for dominance, the axiom is possibly violated by theories with floating feature elements. The introduction of floating elements would thus significantly affect the restrictiveness of the theory, since it requires the relaxation of two axioms of its relations.Precedence in the theory is also irreflexive and transitive, as defined below. Definition (irreflexivity). A relation R is irreflexive if Ra,b entails that a ≠ b. Definition (transitivity). A relation R is transitive if Ra,b and Rb,c entails Ra,c.