2025/07/09 by Uri Andrews, Andrews, Uri, Luca San Mauro +1
Computer Science · #AI-based Problem Solving and Planning #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation
paper · pdf · doi:10.48550/arxiv.2507.06798
openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dialectical systems are a mathematical formalism for modeling an agent updating a knowledge base seeking consistency. Introduced in the 1970s by Roberto Magari, they were originally conceived to capture how a working mathematician or a research community refines beliefs in the pursuit of truth. Dialectical systems also serve as natural models for the belief change of an automated agent, offering a unifying, computable framework for dynamic belief management. The literature distinguishes three main models of dialectical systems: (d-)dialectical systems based on revising beliefs when they are seen to be inconsistent, p-dialectical systems based on revising beliefs based on finding a counterexample, and q-dialectical systems which can do both. We answer an open problem in the literature by proving that q-dialectical systems are strictly more powerful than p-dialectical systems, which are themselves known to be strictly stronger than (d-)dialectical systems. This result highlights the complementary roles of counterexample and contradiction in automated belief revision, and thus also in the reasoning processes of mathematicians and research communities.