 Formalising knowledge as a predicate in a first-order logic is referred to as the syntactic treatment of knowledge. Alternatively, one can choose to formalise knowledge as a modal operator in a suitable modal logic. This is referred to as the semantic treatment of knowledge. In the semantic treatment of knowledge one generally avoids problems of self-reference, and thus inconsistency, but it is at the expense of the expressive power of the formalism (the problems of self-reference are avoided by propositional modal logic not admitting anything equivalent to the diagonal lemma for constructing self-referential formulas).