NML3 : a non-monotonic formalism with explicit defaults

University dissertation from Linköping, Sweden : Linköpings tekniska högskola

Abstract: The thesis is a study of a particular approach to defeasible reasoning based on the notion of an information state consisting of a set of partial interpretations constrained by an information ordering. The formalism proposed, called NML3, is a non-monotonic logic with explicit defaults and is 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 technique 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 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.In addition to NML3, a novel extension of the tableau-based proof technique is presented where a signed formula is tagged with a set of truth values rather than a single truth value. This is useful if the tableau-based proof technique is to be generalized to apply to the class of multi-valued logics. A refutation proof procedure may then be used to check logical consequence for the base logic used in NML3 and to provide a decision procedure for the propositional case of NML3.A survey of a number of non-standard logics used in knowledge representation is also provided. Various formalisms are analyzed in terms of persistence properties of formulas and their use of information structures.

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