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August 13, 20260 citationsOpen Access

ECL₃Q as an Instance of a General Logical Framework: Preliminary Results

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MBMarkus Karl Bauernfeind

Key Points

  • The study aims to classify ECL₃^Q within a framework for many-valued and non-classical logics, exploring its implications and connections to other logical systems.
  • Formalization of a general logical framework for many-valued logics.
  • Investigation of the completeness and incompleteness of ECL₃^Q within this framework.
  • Examination of model amalgamation across branches.
  • A completeness result is established for a restricted fragment of ECL₃^Q.
  • An incompleteness result provides a counterexample to Diaconescu’s generic compactness pattern.
  • Closed result on model amalgamation for the non-deterministic branch is reported.

Abstract

This note reports preliminary results from an ongoing effort to place ECL₃Q — 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 ECL₃Q 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; ECL₃Q 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 ECL₃Q, 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.

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Cite This Study

Markus Karl Bauernfeind (2026) studied this question.

synapsesocial.com/papers/6a7d76652b0e0cff3f63fa8chttps://doi.org/10.5281/zenodo.21889596
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