双值超一致注释逻辑中的证据源解耦：一种用于教育评估的广义PAL2v框架
Decoupling Evidence Sources in Paraconsistent Logic: A Generalized PAL2v Framework for Educational Assessment
- Center for Logic, Epistemology and the History of Science (CLE), State University of Campinas (UNICAMP)（圣保罗州立大学逻辑、认识论与科学史中心）
- Institute of Philosophy and the Humanities (IFCH), State University of Campinas (UNICAMP)（圣保罗州立大学哲学与人文学院）
- Faculdade Israelita de Ciências da Saúde Albert Einstein (FICSAE)（阿尔伯特爱因斯坦以色列健康科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对PAL2v逻辑中证据坐标耦合导致矛盾状态不可达的问题，提出解耦证据源构造，使所有逻辑状态可达，并给出完全决策过程，应用于教育评估以量化学生表现与投入差距。
AI中文摘要：
双值超一致注释逻辑（PAL2v）用一对有利证据和不利证据的程度(μ, λ)来注释命题，这对程度取自一个双格，其四个极点是Belnap和Dunn的值。然而，在应用中，第二个坐标几乎总是被取为第一个坐标的补数，然后将若干这样的注释进行融合。我们表明，这种做法预先决定了矛盾度的符号，与数据无关：对于聚合函数F和G，融合后的矛盾度等于F - G^d，其中G^d是G的德摩根对偶，因此当两者是对偶时，矛盾度恒为零，否则具有恒定符号。特别地，文献中普遍使用的分量最小值仅产生一致的注释，而注释逻辑的合取仅产生精确的注释；十二种逻辑状态中有五种（包括矛盾）在构造上基本上不可达。我们还给出了一个可证明为完全的十二种状态的决策过程，以取代当前使用的不等式列表，后者将大约一半的非极端区域分配给两种状态。然后，我们提出一种构造，其中两个坐标由不相交的证据族计算得出，并表明每种逻辑状态都是可达的。教育评估提供了一个自然的实例，因为总结性工具和形成性工具在制度上是不同的：将考试映射到μ，将脱离参与映射到λ，使得矛盾度等于学生所展示的与其所投入之间的差距。对三个队列概况的模拟说明了这种分类。
英文摘要：
Paraconsistent Annotated Logic with two values (PAL2v) annotates a proposition with a pair $(μ,λ)$ of degrees of favorable and unfavorable evidence, drawn from a bilattice whose four extreme points are the values of Belnap and Dunn. In applications, however, the second coordinate is almost always taken to be the complement of the first, and several such annotations are then fused. We show that this practice determines the sign of the degree of contradiction in advance, independently of the data: for aggregation functions $F$ and $G$ the fused degree of contradiction equals $F-G^{d}$, where $G^{d}$ is the De Morgan dual of $G$, so that it vanishes identically when the two are dual, and has a constant sign otherwise. In particular the componentwise minimum used throughout the literature yields only consistent annotations, and the conjunction of annotated logic only exact ones; five of the twelve logical states, contradiction among them, are essentially unreachable by construction. We also give a decision procedure for the twelve states that is provably total, in place of the inequality lists in current use, which assign two states to about half of the non-extreme region. We then propose a construction in which the two coordinates are computed from disjoint families of evidence, show that every logical state is attainable. Educational assessment provides a natural instance, since summative and formative instruments are institutionally distinct: mapping examinations to $μ$ and disengagement to $λ$ makes the degree of contradiction equal to the gap between what a student demonstrates and what that student invests. Simulations over three cohort profiles illustrate the classification.
