In a classical, boolean or two-valued logic every proposition is either true or false and no other feature of the proposition is relevant. In these the possibility that a proposition is neither true nor false is admitted. Many-Valued Logics Truth functional logics in which there are more than three truth values are also possible. A logic which is not truth functional is sometimes called intensional . These concern necessity and possibility, knowledge and belief, temporal concepts, and many others.
Intuitionistic logics limit the power of proof by contradiction.
These logics have been devised by philosophers dissatisfied with material implication. In a non-monotonic logic it is sometimes possible to derive fewer conclusions when additional premises are made available. For a variety of reasons formal logics usually involve an extra layer of structure above the propositions or sentences which are its subject matter. At this level a sentence may be asserted, or a more complex judgement involving several sentences may be expressed and proven. Frege's Judgements Judgements of the kind we are considering here were first introduced by Frege in his Begriffscrift .