An axiomatization of wansing's expansion of nelson's logic
TLDR
An axiomatization for an expansion of Nelson’s logic motivated by Heinrich Wansing is offered which serves as a base logic for the framework of nonmonotonic reasoning considered by Dov Gabbay and Raymond Turner.Abstract:
A b s t r a c t. The present note offers an axiomatization for an expansion of Nelson’s logic motivated by Heinrich Wansing which serves as a base logic for the framework of nonmonotonic reasoning considered by Dov Gabbay and Raymond Turner. We also show that the expansion of Wansing is not conservative over intuitionistic logic, but at least as strong as Jankov’s logic.read more
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Journal ArticleDOI
A Note on Wansing's expansion of Nelson's logic
TL;DR: In this paper, the author corrects an error made by the author in answering an open problem of axiomatizing an expansion of Nelson's logic introduced by Heinrich Wansing.
References
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Book
Logics for artificial intelligence
Raymond Turner,Will Norman +1 more
TL;DR: This book's goal, to serve as an elementary text and reference work on the applications of nonstandard logics to artificial intelligence, is somewhat more restrictive than what was inferred from the rifle, namely uses of logic in AI.
Journal ArticleDOI
Proof theory of Nelson's paraconsistent logic: A uniform perspective
Norihiro Kamide,Heinrich Wansing +1 more
TL;DR: In this paper, proof systems for Nelson's paraconsistent logic N4 are comprehensively studied and some basic theorems including cut-elimination, normalization and completeness are uniformly proved using various embedding theorem.
Book ChapterDOI
Intuitonistic Basis for Non-Monotonic Logic
Dov M. Gabbay,Dov M. Gabbay +1 more
TL;DR: The semantics seems to be inadequate and there are several counterintuitive results obtained in the system of non-monotonic logic proposed by McDermott and Doyle.
Journal ArticleDOI
The Class of Extensions of Nelson's Paraconsistent Logic
TL;DR: This article studies interrelations between εN4⊥ and the lattice of superintuitionistic logics and the basic subclasses of explosive logics, normallogics, logics of general form and how they relate.
Journal ArticleDOI
Semantics-based Nonmonotonic Inference
TL;DR: This paper discusses Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic base system by Kleene’s three-valued logic and shows that a certain counterintuitive feature of these approaches can be avoided by using Nelson's constructive logic N.
Related Papers (5)
C.I. Lewis, E.J. Nelson, and the modern origins of connexive logic
Edwin D. Mares,Francesco Paoli +1 more