ECL₃^Q as an Instance of a General Logical Framework: Preliminary Results

Abstract

This note reports preliminary results from an ongoing effort to place ECL₃^Q — a three-valued epistemic causal logic with an ontological (not epistemic) third value U, developed independently in Paper I — inside a more general classificatory framework for many-valued and non-classical logics. The guiding question is not whether ECL₃^Q is novel, but how many independently developed logical systems can be recovered as special cases of a single abstract level tree, following an extension-rather-than-replacement principle (in analogy to Newtonian mechanics as a limiting case of relativity). Within this tree, K3, Ł3, Bochvar’s internal connectives, LP, FDE, intuitionistic propositional logic, de Vries’ fuzzy/quantum hierarchy, and supervaluationism are all recovered as special cases; ECL₃^Q occupies one further branch (Level 3), distinguished by an irreversible collapse dynamics. The root of the tree separates two architectures — Nmatrix-based (non-deterministic multifunctions, with truth-functional determinism as a special case) and precisificational — and we report two universal statements holding across this entire space, independent of any specific branch. The framework is formalized institution-theoretically; we report a completeness result for a restricted fragment of ECL₃^Q, a matching incompleteness result for the full language that we present as a counterexample to Diaconescu’s (2017) generic compactness pattern for stratified institutions — based on secondary-source review of the abstract, not verified against full text — and a closed negative result on model amalgamation for the non-deterministic branch. This is a work-in-progress, informal preprint, fully independent of Paper I (currently under review at the Journal of Logic and Computation), with no citation dependency in either direction. Open points are stated explicitly rather than concealed.