Daniel T. Heinze, A-Life Medical, Inc.
Circular definitions and hypotheses about the possible implications of counterfactual assertions are common in natural language. Most logic and ontology systems, however, do not provide meaningful results on definitions with term cycles and, because of limitations in the handling of negation, result in an undefined condition due to counterfactual assertions. L-space is an adaptation of the Scott lattice to computationally express the semantic space metaphor of natural language as described in Langacker’s cognitive grammar. L-space is here presented in terms of its knowledge and truth ordering, showing how it, in fulfilling the modeling requirements of cognitive grammar, provides a solution to the persistent problems associated with term cycles and negation in logic based ontologies. We show that in L-space ontologies, fixpoint calculations on definitions that include the term cycles terminate at the intuitively expected solution. Beyond dealing with term cycles this feature is shown to be of importance for term categorization problems that are faced in representing ontologies for use in natural language processing. Negation in L-space is presented as a fundamental alternative to negation by failure and is compared to classical and strong negation. A method is introduced for using L-space to reason about conditional and counterfactual statements in terms of possible and impossible worlds.