Dynamic Negation, The One and Only
Marco Hollenberg, Albert Visser · 1997
We consider the variety of Dynamic Relation Algebras V(DRA). We show that the monoid of an algebra in this variety determines dynamic negation uniquely. Key words: Dynamic Predicate Logic, relation algebra, modal logic, dynamic logic, finite axiomatization, variety 1 Introduction A Dynamic Relation Algebra or DRA is the algebra of all relations on a given domain D with operations id, the identity or diagonal relation, ?, the empty relation, ;, composition (in the order of application), and dynamic negation ¸. Here: ffl a(¸R)b :, a = b and, for no c, aRc. Subsets of the given domain D can be represented as relations via the standard embedding diag, where diag(X) = fhx; xi j x 2 Xg. The elements of the range of diag are subrelations of the diagonal id. These subrelations are called tests or conditions. If we write dom(R) for the domain of R and (:) c for complementation in D, we have: ¸R = diag((dom(R)) c ). The study of DRA's is motivated by Dynamic Predicate Logic (DPL, see [...