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Doherty, P. and Lukaszewicz, W. (1991). NML3 --- An Non-monotonic Logic with Explicit Defaults. Technical Report LiTH-IDA-R-91-13, Department of Computer and Information Science, Linköping University, Sweden. To appear in the Journal of Applied Non-Classical Logics, 1991. (bibtex),

Abstract: We present a non-monotonic logic with explicit defaults, NML3, characterized by the following features: (1) The use of the strong Kleene three-valued logic as a basis. (2) The addition of an explicit default operator which enables distinguishing tentative conclusions from ordinary conclusions in the object language. (3) The use of the idea of preferential entailment to generate non-monotonic behavior. The central feature of the formalism, the use of an explicit default operator with a model theoretic semantics based on the notion of a partial interpretation, distinguishes NML3 from most of the existing formalisms. By capitalizing on the distinction between tentative and ordinary conclusions, NML3 provides increased expressibility in comparison to many of the standard non-monotonic formalisms and greater flexibility in the representation of subtle aspects of default reasoning. We show this through example. Technically, NML3 belongs to the class of preferential logics. The semantics is model-theoretic with well motivated underlying intuitions and is multi-valued. An explicit default operator is defined with an intuitive declarative semantics. We show (in the context of recent work by Makinson and Kraus et. al. that NML3's consequence relation is well-behaved.


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