Decoupling Evidence Sources in Paraconsistent Logic: A Generalized PAL2v Framework for Educational Assessment

RESUMO

Paraconsistent Annotated Logic with two values (PAL2v) annotates a proposition with a pair $(\mu,\lambda)$ 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 $\mu$ and disengagement to $\lambda$ 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.