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Classical logic is based on the principle of bivalence , that every proposition has exactly one of the two logical values truth or falsity. This finds expression in the two laws: the law of the excluded middle and the law of non-contradiction , With the classical understanding of the connectives, EM and CP may be read as stating that of the two propositions p and ¬ p , at least one is true and at least one is false, respectively. The most natural and straightforward step beyond two-valued logic is to introduce more logical values, thereby rejecting the principle of bivalence. Another, indirect, way consists in challenging the classical laws concerning the sentence connectives and introducing other non-two-valued connectives into the language. Either way, prepositional logic seems fundamental to many-valuedness, rather than its first-order extension. Hence, although there has been interesting research into first-order many-valued logics, we shall confine our discussion here to the 0-order case. While the roots of many-valued logics can be seen in Aristotle-with his famous concern for future contingents and the ‘sea-battle tomorrow’-and traced through the middle ages and the nineteenth century, the real ‘era of many-valuedness’ began in 1920 with the work of Łukasiewicz and Post. This chapter looks at each in turn, and then some others. Łukasiewicz first introduced ... log in or subscribe to read full text