Annotated natural deduction for adaptive reasoning

Patrick Allo, Giuseppe Primiero

Research output: Chapter in Book/Report/Conference proceedingChapterResearchpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationGraham Priest on Dialetheism and Paraconsistency.
PublisherSpringer
Pages409-437
Number of pages29
Volume18
ISBN (Electronic)978-3-030-25365-3
ISBN (Print)978-3-030-25364-6
DOIs
Publication statusPublished - 1 Jan 2019

Publication series

NameOutstanding Contributions to Logic
Volume18
ISSN (Print)2211-2758
ISSN (Electronic)2211-2766

Keywords

  • Adaptive logic
  • Classical recapture
  • Natural deduction
  • Paraconsistent logic

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