超越Belnap-Dunn逻辑的概率：处理间隙、过剩与可靠性
Paraconsistent and paracomplete probabilities: Measuring reliable and unreliable beliefs
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中文总结 AI 辅助
本文提出基于6值paradefinite逻辑LETK⁺的概率函数，利用twist结构语义解释逻辑概率，证明其可靠性与完备性，还给出LETK⁺上Jeffrey更新的语义与句法刻画并证明等价。
中文摘要 AI 辅助
本文引入基于6值 paradefinite（即次协调且次完全）逻辑 LETK⁺ 的概率函数研究。该逻辑是强大且通用的证据与真理逻辑（LET），是经典逻辑与FDE的保守扩张。本文提出的框架允许考虑事件的间隙、过剩与可靠性（或经典性），扩展了Klein、Majer和Rafiee Rad提出的基于FDE的概率详细方案。本方案的显著特征是使用 twist 结构语义，通过这类模型中赋值为每个公式关联的三个或六个区域，自然解释LETK⁺上的逻辑概率。LETK⁺概率函数通过公理和语义定义，获得了可靠性与完备性结果。最后还研究了基于LETK⁺的条件概率，具体提出了LETK⁺概率上Jeffrey更新的语义与句法刻画，并证明二者等价。
英文摘要
In this paper, we introduce the study of probability functions based on the 6-valued paradefinite (i.e., paraconsistent and paracomplete) logic LETK+. This logic is a powerful and versatile Logic of Evidence and Truth (LET) which is a conservative expansion of both classical logic and FDE. The framework introduced here allowed us to consider gaps, gluts, and reliability (or classicality) of the events, extending the detailed proposal for FDE-based probabilities presented by Klein, Majer, and Rafiee Rad. A distinctive feature of our proposal is the use of twist structure semantics, which gives rise to a natural interpretation of logical probabilities over LETK+ in terms of the three or six regions associated with each formula by a valuation in such models. The LETK+-probability functions are defined axiomatically and semantically, obtaining soundness and completeness results, as one would expect. Finally, conditional probabilities based on LETK+ are also studied. Specifically, both a semantic and a syntactic characterization of Jeffrey's update over LETK+-based probabilities is proposed, showing their equivalence.
