辩证神论、博弈论语义学与次协调团队语义学
Dialetheism, Game Theoretic Semantics, and Paraconsistent Team Semantics
摘要：
我们介绍了一个变体的依赖逻辑中的真理定义不存在的获胜策略的支持者（Eloise）在语义游戏中，但在缺乏获胜策略的对手（Abelard）。我们证明了这种语言是一阶逻辑的保守但次协调的扩展，它的有效性问题可以归结为一阶逻辑的有效性问题，它能够表达自己的真值和有效性谓词，并且它在表达上等价于通用二阶逻辑。此外，我们证明了一个次协调的非依赖逻辑公式是一致的当且仅当它是等价于一些一阶逻辑句子;另一方面，我们表明，所有的次协调依赖逻辑句子等价于一些一阶句子就真（但不一定就假）。
英文摘要：
We introduce a variant of Dependence Logic in which truth is defined not in terms of existence of winning strategies for the Proponent (Eloise) in a semantic game, but in terms of lack of winning strategies for the Opponent (Abelard). We show that this language is a conservative but paraconsistent extension of First Order Logic, that its validity problem can be reduced to that of First Order Logic, that it capable of expressing its own truth and validity predicates, and that it is expressively equivalent to Universal Second Order Logic. Furthermore, we prove that a Paraconsistent Non-dependence Logic formula is consistent if and only if it is equivalent to some First Order Logic sentence; and we show that, on the other hand, all Paraconsistent Dependence Logic sentences are equivalent to some First Order sentence with respect to truth (but not necessarily with respect to falsity).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
