English

Abstract

Systems for qualitative spatial reasoning (QSR) are usually formulated as relation algebras, and reasoning in such systems is performed by constraint-satisfaction techniques. While this is often adequate, it is a rather inexpressive framework that cannot model and solve many spatial reasoning problems; it can also complicate the combination of different spatial formalisms, e.g., the combination of topological with metric primitives, or absolute orientation with relative orientation. Here we suggest an alternative approach, whereby spatial information is expressed in a rich quantified 3-valued logic, equipped with a novel semantics for dealing with incomplete information. Decidability is ensured by a systematic compilation into propositional logic and the use of SAT solvers. To illustrate, we define and implement a new system for two-dimensional positional reasoning that combines Frank’s cardinal-direction calculus, the flip-flop calculus for reasoning about relative orientation, and various new positional primitives. Unlike previous work, the system uses diagrams as well as symbolic formulas. In particular, the logic we introduce is heterogeneous, meaning that it combines symbolic and diagrammatic representation and inference. 1 A Hybrid System For Reasoning