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Annotated natural deduction for adaptive reasoning

Book Contribution - Chapter

We present a multi-conclusion natural deduction calculus characterizing the dynamic reasoning typical of Adaptive Logics. The resulting system AdaptiveND is sound and complete with respect to the propositional fragment of adaptive logics based on CLuN. This appears to be the first tree-format presentation of the standard linear dynamic proof system typical of Adaptive Logics. It offers the advantage of full transparency in the formulation of locally derivable rules, a connection between restricted inference-rules and their adaptive counterpart, and the formulation of abnormalities as a subtype of well-formed formulas. These features of the proposed calculus allow us to clarify the relation between defeasible and multiple-conclusion approaches to classical recapture.

Book: Graham Priest on Dialetheism and Paraconsistency.
Series: Outstanding Contributions to Logic
Volume: 18
Pages: 409-437
Number of pages: 29
ISBN:978-3-030-25364-6
Publication year:2019
Keywords:Adaptive logic, Classical recapture, Natural deduction, Paraconsistent logic