This paper answers the philosophical contentions defended in Horsten and Welch (2007, Synthese, 158, 41-60). It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.

In this paper I present two new strategies for inconsistencyadaptive logics: the reliable sufficient information strategy of ACLuN3 and the minimally abnormal sufficient information strategy of ACLuN4. I give proof theory and semantics for both ACLuN3 and ACLuN4. I also compare them with the well-known inconsistency-adaptive logics ACLuN1 and ACLuN2. * Research Assistant of the Fund for Scientific Research-Flanders (Belgium)(F.W.O.). 1 See [2], although the paper was written much earlier. For a study of the predicative version see [5]. A survey of the domain is presented in Batens [6]. For an informal description and the relation with argumentation, see [4].

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