揭示累积命题依赖逻辑的模型表征，统一多种逻辑的推理框架。
Representation Theorems for Cumulative Propositional Dependence Logics
- 用累积模型刻画命题依赖逻辑的蕴含关系
- 团队语义下的累积逻辑等价于非对称累积模型
- 为无否定和蕴含的累积逻辑提供通用证明方法
本文建立了累积命题依赖逻辑与具有团队语义的累积命题逻辑的表示定理。累积逻辑由系统C定义。对于命题依赖逻辑，我们证明系统C的蕴含关系恰好由Kraus、Lehmann和Magidor提出的累积模型所刻画。另一方面，我们证明具有团队语义的累积命题逻辑的蕴含关系恰好由累积且非对称模型所刻画。此外，该类逻辑还等价于基于经典语义的命题逻辑累积系统。这些证明方法可推广至其他不含否定和实质蕴含的累积逻辑的表示定理证明。
原文摘要 · Abstract (English)
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.
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