Submission Type:
Article in Special Issue (note in cover letter)
Cover Letter:
Dear Professors Belle, Liu, Dhami, Kuželka and Tsamoura,
I submit ‘Pair-Valued Deontic Semantics and Rule-Regularised Learning from Conflicting Norms’ for the special issue on Neurosymbolic AI: First-Order Logic and Beyond.
The paper defines a pair-valued, finite-domain, first-order deontic semantics in which conflicting evidence is a value, and relates it to interval-bound semantics. It proves agreement with classical Kripke evaluation on Boolean valuations, non-explosion, modal monotonicity and, for crisp accessibility, containment of inconsistency, with an evaluation cost quadratic in the number of worlds. A controlled synthetic study evaluates a single-ideal-world reduction with one two-head network under three loss configurations: rule constraints improve derived-norm accuracy over data alone, and omitting a consistency regulariser improves source-norm accuracy and conflict detection when conflicts are frequent, while the regularised model stays better on derived norms. The study does not evaluate learned accessibility, general first-order inference or source-provenance explanations, and the paper says so. It addresses the special issue’s topics on modal and first-order reasoning and logic-based knowledge in learning.
The manuscript is original, has not been published or submitted elsewhere, and is not under consideration by another journal. Code, data generators and per-seed summary metrics are provided as supplementary material and deposited at https://github.com/sgurfinkel1-dev/paraconsistent-deontic-networks (commit c6d7fb305c979d8e358e5c6f5f92f2d9d7a1d965; currently private). Raw generated examples and model checkpoints are not archived.
Sincerely,
Saul Gurfinkel Marques de Godoy
sgurfinkel@alumni.usp.br