extending the "for all" operator to the Law of Excluded Middle; it allows instances of the "Law", but not its generalization to an infinite domain of discourse. Intuitionistic logic 'Intuitionistic logic', sometimes more generally called constructive logic, is a paracomplete symbolic logic that differs from classical logic by replacing the traditional concept of truth with the concept of constructive provability. The generalized law of the excluded middle is not part of the execution of intuitionistic logic, but neither is it negated. Intuitionistic logic merely forbids the use of the operation as part of what it defines as a "constructive proof", which is not the same as demonstrating it invalid (this is comparable to the use of a particular building style in which screws are forbidden and only nails are allowed; it does not necessarily disprove or even question the existence or usefulness of screws, but merely demonstrates what can be built without them). Paraconsistent logic 'Paraconsistent logic' refers to so-called contradiction-tolerant logical systems in which a contradiction does not necessarily result in trivialism. In other words, the principle of explosion is not valid in such logics. Some (namely the dialetheists) argue that the law of non-contradiction is denied by dialetheic logic. They are motivated by certain paradoxes which seem to imply a limit of the law of non-contradiction, namely the liar paradox. In order to avoid a trivial logical system and still allow certain contradictions to be true, dialetheists will employ a paraconsistent logic of some kind. Three-valued logic TBD cf Three-valued logic try this A Ternary Arithmetic and Logic – Semantic Scholar Modal propositional calculi (cf Kleene 1967:49): These "calculi" include the symbols ⎕A, meaning "A is necessary" and ◊A meaning "A is possible". Kleene states that: "These notions enter in domains of thinking where there are understood to be two different kinds of "truth", one more universal or compelling than the other ... A zoologist might declare that it is impossible that salamanders or any other living creatures can survive fire; but possible (though untrue) that unicorns exist, and possible (though improbable) that abominable snowmen exist." Fuzzy logic 'Fuzzy logic' is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. See also Algebra of concepts References Aristotle, "The Categories", Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Vol. 1, Loeb Classical Library, William Heinemann, London, UK, 1938. Aristotle, "On Interpretation",