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This paper presents a novel SHOI tableau calculus which incorporatesalgebraic reasoning for deciding ontology consistency. Numerical restrictionsimposed by nominals, existential and universal restrictions are encoded into aset of linear inequalities. Column generation and branch-and-price algorithmsare used to solve these inequalities. Our preliminary experiments indicate thatthis calculus performs better on SHOI ontologies than standard tableau methods.

Handling Nominals and Inverse Roles using Algebraic Reasoning