Fuzzy Quantification over OWL Ontologies and Knowle... | AI Research

Fuzzy Quantification over OWL Ontologies and Knowledge Graphs
This paper introduces a flexible framework designed to evaluate fuzzy quantification queries across both standard and fuzzy ontologies, as well as knowledge graphs. While traditional logic systems are often limited to simple existential or universal quantifiers—such as "some" or "all"—this approach enables the retrieval of individuals based on more nuanced, human-like expressions. By supporting both Type I and Type II fuzzy quantified queries, the framework allows systems to handle vague requirements, such as finding bands where "almost all" albums belong to a specific genre, rather than being restricted to binary "yes or no" conditions.

A Versatile Approach to Vague Queries

The core strength of this framework is its adaptability. It is designed to be agnostic, meaning it functions independently of the specific type of quantifier used, the underlying evaluation method, or the data source format. Whether the system is interacting with a standard OWL ontology or an RDFS knowledge graph, the framework provides a consistent way to process queries. It achieves this by bridging the gap between classical knowledge bases and fuzzy logic, allowing users to incorporate fuzzy datatypes and quantifiers into their existing semantic reasoning systems.

Evaluation Methods

The framework supports several established methods for calculating the truth degrees of fuzzy queries. These include Zadeh’s method, which relies on the "sigma count" to determine the cardinality of fuzzy sets; Yager’s OWA-based method, which uses ordered weighted averaging to aggregate information; and the GD method, which utilizes specific fuzzy cardinality definitions to evaluate queries. By offering these different mathematical approaches, the framework provides researchers and developers with the tools to choose the evaluation strategy that best fits their specific data and application needs.

Implementation and Research Support

To facilitate further research and practical application, the authors have developed and released Q2S2, a publicly accessible implementation of this system. This tool is intended to serve as a foundation for future studies in the field of Knowledge Representation and Reasoning. By providing a working prototype, the authors aim to lower the barrier for integrating fuzzy quantification into intelligent systems, enabling more sophisticated and flexible data retrieval in domains where information is inherently imprecise or uncertain.