A resolution-theorem-prover (RTP) evaluates the validity (truthfulness) of conjectures against a set of axioms in a knowledge base. When given a conjecture, an RTP attempts to resolve the negated conjecture with axioms from the knowledge base until the prover nds a contradiction. If the RTP nds a contradiction between the axioms and a negated conjecture, the conjecture is proven. The order in which the axioms within the knowledge-base are evaluated signicantly impacts the runtime of the program, as the search-space increases exponentially with the number of axioms. Ontologies, knowledge bases with semantic (and predominantly hierarchical) structures, describe objects and their relationships to other objects. For example, a 'Sedan' class might exist in a sample ontology with 'Automobile' as a parent class and 'Minivan' as a sibling class. Currently, hierarchical structures within an ontology are not taken into account when evaluating the relevance of each axiom. Instead, each predicate is automatically assigned a weight based on a heuristic measure (such as the number of terms or the frequency of predicates relevant to the conjecture) and axioms with higher weights are evaluated rst. My research aims to intelligently select relevant axioms within a knowledge-base given a structured relationship between predicates. I have used semantic hierarchies passed to a weighting function to assign weights to each predicate. The research aims to design heuristics based upon the semantics of the predicates, rather than solely the syntax of the statements. I developed weighting functions based upon various parameters relevant to the ontological structure of predicates contained in the ontology, such as the size and depth of a hierarchy based upon the structure. The functions I have designed calculate weights for each predicate and thus each axiom in attempts to select relevant axioms when proving a theorem. I have conducted an experimental study to determine if my methods show any improvements over current reasoning methods. Results for the experiments conducted show promising results for generating weights based on semantic hierarchies and encourage further research.
Small, Stanley, "Exploring Semantic Hierarchies to Improve Resolution Theorem Proving on Ontologies" (2019). Honors College. 538.