A New Real-Time Algorithm to Extend DL Assertional Formalism to Represent and Deduce Entities in Robotic Soccer

Creating, maintaining, and deducing accurate world knowledge in a dynamic, complex, adversarial, and stochastic environment such as the RoboCup environment is a demanding task. Knowledge should be represented in real-time (i.e., within ms) and deduction from knowledge should be inferred within the same time constraints. We propose an extended assertional formalism for an expressive \(\mathcal {SROIQ}(\mathcal {D})\) Description Logic to represent asserted entities in a lattice structure. This structure can represent temporal-like information. Since the computational complexity of the classes of description logic increases with its expressivity, the problem demands either a restriction in the expressivity or an empirical upper bound on the maximum number of axioms in the knowledge base. We assume that the terminological/relational knowledge changes significantly slower than the assertional knowledge. Henceforth, using a fixed terminological and relational formalisms and the proposed lattice structure, we empirically bound the size of the knowledge bases to find the best trade-off in order to achieve deduction capabilities of an existing description logic reasoner in real-time. The queries deduce instances using the equivalent class expressions defined in the terminology. We have conducted all our experiments in the RoboCup 3D Soccer Simulation League environment and provide justifications of the usefulness of the proposed assertional extension. We show the feasibility of our new approach under real-time constraints and conclude that a modified FaCT++ reasoner empirically outperforms other reasoners within the given class of complexity.