2018/05/08 by Yijia Chen, Abdallah Saffidine, Chen, Yijia +3
Computer Science · #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.1805.02912
openalex publication_date 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.