Layer four
Logic.
What follows from what.
Entailment and opposition between the propositions that sentences express, decided where they can be decided and measured where they cannot.
Chapter 1
The Famulus Normal Form
Nothing follows from a sentence. Entailment and opposition hold between the propositions that sentences express. To decide such relations at the scale of a collection, the Famulus Normal Form writes the proposition a sentence expresses as literals over atoms — a predicate with its roles — so that a relation between two propositions becomes a join in DuckDB (2,825 lines).
Where the normal form decides, the decision carries its literals; where it cannot, it says so, and a classifier may be consulted. The specification is the technical document The Famulus Normal Form (13 pages).
Chapter 2
Measuring classifiers of logical relations
famulus-logic is a test bench for classifiers of logical relations between the propositions of PDAI collections: the normal form, natural-language inference models, language models, and a cascade that asks the cheaper one first. Every prediction is stored with its run, so a leaderboard compares classifiers on the same cases (5,243 lines, 51 test functions).
The bench is described in famulus-logic (23 pages, in German); an audit of needle-in-a-haystack questions on Kármán sentences is Nadel im Heuhaufen (10 pages). The epistemology behind both — why retrieval cannot establish truth, and what must take its place — is the draft Computational Epistemology: Foundations (20 pages).