We give a simple example of a variety V of modal algebras that is canonical but cannot be axiomatised by canonical equations or first-order sentences. We then show that the variety RRA of representable relation algebras, although canonical, has no canonical axiomatisation. Indeed, we show that every axiomatisation of these varieties involves infinitely many noncanonical sentences. Using probabilistic methods...

This paper deals with aspects of my doctoral dissertation 1

this paper an argument is a two-part system composed of a set of propositions P (the premise-set) and a single proposition c (the conclusion). The expression `c is a [logical] consequence of P' is used with the same meaning as the expression `c is [logically] implied by P'. The expressions `is a logical consequence of ' and the converse `implies' are relational. Often, I shall be talking in the same sense of validity of an argument. Validity is a property of arguments; an argument with premise-set P and conclusion c is valid if and only if P implies c; i.e., c is a logical consequence of P. Notice that this notion of argument is strictly ontic; it does not involve any agent that thinks, determines or establishes that a given proposition is or is not a consequence of a given set of propositions