Logical Metrics¶

Logical health and performance metrics for LNN models.

jlnn.utils.metrics.contradiction_degree(interval: Array) → Array[source]¶

Calculates the degree of logical contradiction within a truth interval.

In LNN, a contradiction occurs when the lower bound (L) exceeds the upper bound (U), meaning the evidence for truth is greater than the evidence for possibility.

Parameters:: interval (jnp.ndarray) – Truth interval tensor [L, U].
Returns:: Magnitude of contradiction (max(0, L - U)).
Return type:: jnp.ndarray

jlnn.utils.metrics.uncertainty_width(interval: Array) → Array[source]¶

Calculates the width of the uncertainty gap (U - L).

A width of 0.0 represents a precise truth value (classical logic), while 1.0 represents complete ignorance (unknown).

Parameters:: interval (jnp.ndarray) – Truth interval tensor [L, U].
Returns:: The distance between upper and lower bounds.
Return type:: jnp.ndarray

This module defines metrics for quantifying the quality of logical reasoning.

Contradiction Degree: Measures the extent of violation of the axiom \(L \le U\). A value of 0 indicates a consistent model.
Uncertainty Width: Measures the degree of “ignorance” in the model. The wider the interval \(U - L\), the less information the model has about a given fact.