Volume II: New advances in Logics of Formal Inconsistency

Abstract

Contradictions crop up in an impressive number of real-life contexts of reasoning. On one hand, databases and other formalisms for knowledge representation very often display incomplete information. In many cases, this is remedied by appealing to the so-called closed-world assumption, which means that what is not currently known to be true, is taken to be false. But formalisms for knowledge representation may also contain conflicting (that is, contradictory) information. This may be caused by excessive, incoherent, or vague stipulations. There is, however, no philosophical protection against contradictory information (any analog of the closed-world assumption): standard logic is inflexible against contradictions—the classical logic commandment known as the Principle of Explosion orders that from a contradiction anything should be derived.