Comparing Dialectical Systems: Contradiction and Counterexample in Belief Change (Extended Version)
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| Format: | Preprint |
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2025
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| _version_ | 1866912473046581248 |
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| author | Andrews, Uri Mauro, Luca San |
| author_facet | Andrews, Uri Mauro, Luca San |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_06798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparing Dialectical Systems: Contradiction and Counterexample in Belief Change (Extended Version) Andrews, Uri Mauro, Luca San Artificial Intelligence Logic 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. |
| title | Comparing Dialectical Systems: Contradiction and Counterexample in Belief Change (Extended Version) |
| topic | Artificial Intelligence Logic |
| url | https://arxiv.org/abs/2507.06798 |