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[2602.21360] Representation Theorems for Cumulative Propositional Dependence Logics
Summary
This paper presents representation theorems for cumulative propositional dependence logic and team semantics, establishing key equivalences in logic models.
Why It Matters
Understanding representation theorems in cumulative propositional dependence logics is crucial for advancing logical frameworks in computer science and artificial intelligence. These findings can enhance the application of logic in various computational models and improve reasoning systems.
Key Takeaways
- Establishes representation theorems for cumulative propositional dependence logic.
- Shows that System C entailments are captured by cumulative models.
- Demonstrates equivalence of cumulative propositional logics with team semantics.
- Provides foundational proofs for future representation theorems in cumulative logics.
- Impacts the understanding of logic without negation and material implication.
Computer Science > Logic in Computer Science arXiv:2602.21360 (cs) [Submitted on 24 Feb 2026] Title:Representation Theorems for Cumulative Propositional Dependence Logics Authors:Juha Kontinen, Arne Meier, Kai Sauerwald View a PDF of the paper titled Representation Theorems for Cumulative Propositional Dependence Logics, by Juha Kontinen and 2 other authors View PDF HTML (experimental) Abstract:This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. Cumulative logics are famously given by System C. For propositional dependence logic, we show that System C entailments are exactly captured by cumulative models from Kraus, Lehmann and Magidor. On the other hand, we show that entailment in cumulative propositional logics with team semantics is exactly captured by cumulative and asymmetric models. For the latter, we also obtain equivalence with cumulative logics based on propositional logic with classical semantics. The proofs will be useful for proving representation theorems for other cumulative logics without negation and material implication. Subjects: Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI) MSC classes: 03B70, 03B62 ACM classes: I.2.3; F.4.1 Cite as: arXiv:2602.21360 [cs.LO] (or arXiv:2602.21360v1 [cs.LO] for this version) https://doi.org/10.48550/arXiv.2602.21360 Focus to learn more arXiv-issued DOI via DataCite (pending registration) ...
