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[ÇóÖú]°ïÎÒ¿´¿´Õâ¶ÎµÄÒâ˼ In a few words, paraconsistent logics (PL) are the logics of inconsistent but non-trivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well-formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. Roughly speaking, in a trivial theory `everything' (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems like intuitionistic logic, inconsistency entails triviality, and conversely. So, how can we speak of inconsistent but non-trivial theories? Of course, by changing the underlying logic to one which admits inconsistency without making the system trivial. Paraconsistent logics do just this job. Our use of terms like `consistency', `inconsistency', `contradictory' and simi- lar ones is syntactical, which is in accordance with the original metamathemat- ical terminology of Hilbert and his school. In order to treat such terms from a semantic point of view, in the ¯eld of paraconsistency, one must be able to build, ¯rst, a paraconsistent set theory. This is possible, as we will see, al- though most semantics for paraconsistent logics are classical, i.e., constructed inside classical set theories. So, to begin with, it is best to employ the above terms syntactically. ÉÏÃæµÄ"inconsistency entails triviality"ÊÇʲôÒâ˼?    Êղؠ  ·ÖÏí   ¶¥(0)

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