Quantitative Spatial Reasoning for General Intelligence

One of the basic requirements of an intelligent agent is the ability to represent and reason about space. While there are a number of approaches for achieving this goal, the recent gains in efficiency of the Satisfiability approach have made it a popular choice. Modern propositional SAT solvers are efficient for a wide variety of problems. However, conversion to propositional SAT can sometimes result in a large number of variables and/or clauses. Diagrams represent space as collections of points (regions) while preserving their overall geometric character. This representation allows reasoning to be performed over (far fewer number of) regions instead of individual points. In this paper, we show how the standard DPLL algorithm augmented with diagrammatic reasoning can be used to make SAT more efficient when reasoning about space. We present DPLL-S, a complete SAT solver that utilizes diagrammatic representations when reasoning about space, and evaluate its performance against other SAT solvers.