Reasoning Using Exclusion. An Extension of Clausal Form.

Abstract : In formalizing knowledge for common sense reasoning, one often needs to partition some domain. An instance of this from the block's world is the statement 'All blocks are one of held, on the table, or on another block.' Although we can write such an axiom in predicate calculus using the standard logical connectives, or in clause form as input to a resolution theorem prover, such representations are highly space inefficient. A generalized clause form is presented that allows for the compact representation of arbitrary partitions, along with a set of corresponding inference rules whose soundness and refutation completeness are proven. Additionally, an implementation of a subset of these rules is described that demonstrates their utility with certain kinds of common sense rule bases. (Author)