The logical approach to evidence evaluation is an assessment process that focuses on the evidence, rather than directly addressing any propositions that might ‘explain’ that evidence. In other words, the examiner uses their expert knowledge and ability to determine the likelihood of the evidence (under competing hypotheses or propositions). Likelihood in this context means the conditional probability of the evidence given the hypotheses of interest. It is a system of logical reasoning.
I’ve posted on this topic a few times. Be sure to read my “Introduction to the Logical Approach to Evidence Evaluation”, as well as “Propositions — key to the evaluation process” and “When is a ‘Bayesian’ not a ‘Bayesian’?” This approach to evidence evaluation is also explained in the ENFSI Guideline for Evaluative Reporting.