Nonmonotonic reasoning: Semantics and applications to induction.

This thesis is an investigation of the formalization of nonmonotonic reasoning in two important aspects of human and machine intelligence, namely, default reasoning and induction. Two logics of default reasoning are examined in particular: default logic and circumscription. A semantics for default logic is developed and completeness and soundness results are derived. The relationship between default logic and circumscription is examined in terms of circumscriptive extension of a default theory, which defines the extension of a default theory in the spirit of circumscription. Circumscriptive extension is shown to be a generalization of the original circumscription. It has also been shown that a circumscriptive extension of a default theory is equivalent to a default extension of the default theory, provided that the domain-closure assumption and the unique-names assumption hold. A form of induction, concept learning using the version space approach, is formalized as nonmonotonic reasoning. A consistent concept axiom is defined as a representation of a version space--a set of all the concept descriptions consistent with each of the training instances. Computation of the consistent concept axiom is also discussed. Specifically, for a frequently used syntactical bias, the conjunctive bias, it has been shown that the consistent concept axiom can be reduced to a first-order sentence.Ph.D.Computer, Information, and Control EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105766/1/9208627.pdfDescription of 9208627.pdf : Restricted to UM users only