论文标题
关于证据和真相的六值逻辑，扩展了Belnap-Dunn四名逻辑
On six-valued logics of evidence and truth expanding Belnap-Dunn four-valued logic
论文作者
论文摘要
本文的主要目的是将证据和真理Letk+和Letf+的逻辑与声音，完整且可决定的六值确定性语义一起介绍。这些逻辑扩展了逻辑列表和经典性的传播规则，这是表达经典性运算符o从较不复杂到更复杂的句子的推论，反之亦然。此处提出的六值语义扩展了Belnap-Dunn逻辑的4个值，另外2个值代表（正和负）可靠信息。通过基于掉期结构的Nmatrices获得了六值的非确定性语义，然后通过对Letk的语义施加限制来获得Letk+的六值语义。这些限制与扩展Letk的经典性传播规则完全相对应。逻辑LETF+作为Letk+的无暗示片段获得。我们还表明，Letk+和Letf+的6个值定义了一个晶格结构，该晶格结构扩展了由Belnap-Dunn四量化逻辑定义的晶格L4，上面提到的另外2个值，直观地解释为正面和负面的可靠信息。最后，我们还表明，Letk+是可blok-bigozzi代数，其无暗示的片段LETF+与参考石材代数的学位保留逻辑相吻合。
The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules of propagation of classicality, which are inferences that express how the classicality operator o is transmitted from less complex to more complex sentences, and vice-versa. The six-valued semantics here proposed extends the 4 values of Belnap-Dunn logic with 2 more values that intend to represent (positive and negative) reliable information. A six-valued non-deterministic semantics for LETK is obtained by means of Nmatrices based on swap structures, and the six-valued semantics for LETK+ is then obtained by imposing restrictions on the semantics of LETK. These restrictions correspond exactly to the rules of propagation of classicality that extend LETK. The logic LETF+ is obtained as the implication-free fragment of LETK+. We also show that the 6 values of LETK+ and LETF+ define a lattice structure that extends the lattice L4 defined by the Belnap-Dunn four-valued logic with the 2 additional values mentioned above, intuitively interpreted as positive and negative reliable information. Finally, we also show that LETK+ is Blok-Pigozzi algebraizable and that its implication-free fragment LETF+ coincides with the degree-preserving logic of the involutive Stone algebras.
