Hypertableau Reasoning for Description Logics
This work addresses performance bottlenecks in knowledge representation for applications like the Semantic Web, representing an incremental advancement in reasoning methods.
The paper tackles inefficiencies in tableau-based reasoning for the description logic SHOIQ^+, focusing on reducing nondeterminism and model size, resulting in significant performance improvements over state-of-the-art reasoners on several ontologies.
We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies.