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 multipleconclusion approaches to classical recapture.
Annotated Natural Deduction for Adaptive Reasoning / P. Allo, G. Primiero (OUTSTANDING CONTRIBUTIONS TO LOGIC). - In: Graham Priest on Dialetheism and Paraconsistency / [a cura di] C. Başkent, T. Macaulay Ferguson. - [s.l] : Springer, 2020. - ISBN 9783030253646. - pp. 409-437 [10.1007/978-3-030-25365-3_19]
Annotated Natural Deduction for Adaptive Reasoning
G. Primiero
2020
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 multipleconclusion approaches to classical recapture.File | Dimensione | Formato | |
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