The Complexity of Limited Belief Reasoning -- The Quantifier-Free Case
This addresses the problem of unrealistic logical omniscience in AI and knowledge representation, providing insights into tractability for researchers in computational logic and AI.
The paper tackles the computational complexity of reasoning with limited belief levels in epistemic logic, showing that it is tractable for constant levels but becomes PSPACE-complete when the level is part of the input, and refines this using parameterized complexity theory.
The classical view of epistemic logic is that an agent knows all the logical consequences of their knowledge base. This assumption of logical omniscience is often unrealistic and makes reasoning computationally intractable. One approach to avoid logical omniscience is to limit reasoning to a certain belief level, which intuitively measures the reasoning "depth." This paper investigates the computational complexity of reasoning with belief levels. First we show that while reasoning remains tractable if the level is constant, the complexity jumps to PSPACE-complete -- that is, beyond classical reasoning -- when the belief level is part of the input. Then we further refine the picture using parameterized complexity theory to investigate how the belief level and the number of non-logical symbols affect the complexity.