 The belief-representing sentences form a language. (As is usual in logic, the language is identified with the set of all sentences it contains.) Sentences, i.e. elements of this language, will be represented by lowercase letters \((p, q\ldots)\) and sets of sentences by capital letters. This language contains the usual truth-functional connectives: negation \((\neg)\), conjunction \((\amp)\), disjunction \((\vee)\), implication \((\rightarrow)\), and equivalence (\(\leftrightarrow\)). \(\smbot\) denotes an arbitrary contradiction (“falsum”), and \(\smtop\) an arbitrary tautology.