Presented at 1st World Conference and School on Universal Logic (Montreux)

Abstract. Through their development, adaptive logics (see [1]) have often been devised as modal adaptive logics. That is, a modal logic L strengthened with the provisional application of a rule which is not in L itself (e.g.: <>A => [ ]A). Logical systems using such an approach include inconsistency-adaptive logics based on Jaskowski’s non-adjunctive approach [6], and logics for compatibility [2]. While non-modal adaptive logics generally succeed in providing a natural reconstruction of reasoning, proof-formats for modal adaptive logics lack the same intuitiveness. Basically the drawbacks of the proof-formats stem from adaptive logics’ reliance on a purely syntactic use of modal logics, thus leaving some natural (semantic) insights in modal languages aside. Compared to other adaptive logics (essentially the original inconsistency-adaptive logic ACLuN1) part of the appealing naturalness of dynamic proofs is lost (partly because the rules are defined indirectly with respect to the existence of a Hilbert-style proof). The main purpose of this paper is to provide a labelled proof-format for modal adaptive logics which does not suffer from the mentioned drawbacks.