 Once there are two different analyses of a relation of logical consequence, one can ask about possible interactions, and we’ll do that next. One can also ask what general features such a relation has independently of its analysis as proof-theoretic or model-theoretic. One way of answering this question goes back to  Tarski,  who introduced the notion of consequence operations. For our purposes, we note only some features of such operations. Let \(Cn(X)\) be the consequences of \(X\). (One can think of the operator \(Cn\) as deriving from a prior consequence relation which, when taking \(X\) as ‘input (or premise)’ set, tells you what follows from \(X\). But one can also see the ‘process’ in reverse, and a key insight is that consequence relations and corresponding operations are, in effect, interdefinable. See the entry on  algebraic propositional logic  for details.) Among some of the minimal conditions one might impose on a consequence relation are the following two (from Tarski):