Nonmonotonic Reasoning and Changes of Belief

Abstract

Deductive reasoning is truth-preserving reasoning, that is, a deductive inference from a premise set Prem to a conclusion Con, Prem ⊢ Con, is valid if and only if it holds in every possible situation, or ‘model’ respectively, that whenever the premises are true, the conclusion is true. As a consequence, deductive reasoning is monotonic, that is, whenever Prem ⊢ Con is valid, then also X, Prem ⊢ Con remains valid for every possible new information expressed by a sentence X, may X be true or false. So the validity of a deductive inference is independent from any possible information not contained in the premise set, and hence independent from the context of background knowledge. In this sense, the validity of a deductive inference is a ‘local’, or a ‘modular’ notion, and not a ‘global’, or a ‘holistic’ notion.¹