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Semantics-based nonmonotonic inference. (English) Zbl 0839.03012
D. M. Gabbay [“Intuitionistic basis for non-monotonic logic”, Lect. Notes Comput. Sci. 138, 260-273 (1982; Zbl 0481.68091)] suggested defining a specific nonmonotonic inference relation in terms of a possibility operator “it is consistent to assume at this stage that” in the context of intuitionistic propositional logic. However, this turned out to have certain counterintuitive features, as also did a subsequent variant of Turner using Kleene’s three-valued logic. The author proposes another variant in terms of Nelson’s constructive logic.

MSC:
03B60 Other nonclassical logic
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