Paraconsistent Logic and AI models

mleyvaz
Tue, 28 Apr 2026 04:54:09 +0000

Hi John6666 and Daniel,

Joining this thread late but with real interest, because the diagnosis John6666 laid out maps almost one-to-one onto a research program some of us have been developing in the Latin American paraconsistent and neutrosophic tradition for several years. I think it can save Daniel some reinvention and give John6666 some references he may find useful.

Three quick observations:

1. The fuzzy / paraconsistent distinction is exactly right — and there is a third primitive missing from the discussion: indeterminacy.

John6666 is correct that conflating fuzzy logic with paraconsistency is the single biggest weakness in the article. But the cleanest way out is not to pick one or the other — it is to adopt a framework that already separates them axiomatically. Neutrosophic logic (Smarandache, 1998, 2005) decomposes any proposition into an independent triple (T, I, F) — Truth, Indeterminacy, Falsity — where the standard fuzzy/probabilistic constraint T + I + F = 1 is explicitly dropped. That single move buys you:

T + F > 1 → paraconsistency (genuine contradiction without explosion)

T + I + F < 1 → incompleteness / missing evidence

I high alone → vagueness or underdetermination

T high, I low, F low → confident assertion

So the four failure modes John6666 identifies (vagueness, inconsistency, uncertainty, deduction) are not four separate logics that need to be glued together — they are different regions of a single (T, I, F) space, plus a deductive layer on top. This is much closer to John6666’s “logical pluralism” conclusion than to a one-logic-replaces-all stance.

2. “Epistemic states that evolve through reasoning” already has a name.

The pre-output judgment layer John6666 sketches — classify → route → verify → return epistemic status — is essentially what we have been formalizing as Dynamic Epistemic Logic for LLMs (LED): the (T, I, F) state of a model is not static, it transitions through reasoning steps under three operators — Refinement (I decreases as evidence accumulates), Conflict (incompatible (T, I, F) tuples from different sources), and Resolution (collapse toward a more determinate state). Chain-of-Thought becomes a sequence of epistemic transitions; Mixture-of-Experts becomes aggregation of parallel epistemic states; abstention becomes a thresholded decision on I. The architecture John6666 is describing in his Step 1–4 is, in this language, the operational semantics of LED.

3. There is a concrete UQ implementation already published.

For Daniel’s proof-of-concept Doninha, the relevant prior work is NeutrosophicUQ — a paraconsistent neutrosophic uncertainty quantification framework for LLMs that uses hierarchical clustering with cosine similarity over stochastically sampled responses to extract (T, I, F, C) tuples. Unlike semantic entropy (Farquhar et al., 2024, Nature), which collapses everything to a scalar, this preserves the typology of failure: consensus vs. contradiction vs. ambiguity vs. missing information. It is model-agnostic and works through any LLM API. Daniel — if you want a head start instead of building from scratch, this is where I would point you.

On John6666’s substantive critique: I agree with almost all of it. The “Boolean syllogism machine” framing of LLMs is wrong, the AGI-impossibility move is overreach, and the strongest version of the article is architectural and epistemological, not metaphysical. The one place I would push back gently is on framing this as purely a Western neurosymbolic problem. The Latin American paraconsistent tradition (da Costa, Carnielli, Coniglio, Miró Quesada) and the neutrosophic program (Smarandache, and a growing community across Cuba, Ecuador, Mexico, Peru) have been working on exactly these questions — non-explosion under contradiction, indeterminacy as a primitive, plural logical regimes — for decades. The mainstream NeSy literature is only recently catching up.

References if useful:

Smarandache, F. (2005). A Unifying Field in Logics: Neutrosophic Logic. American Research Press.

Leyva-Vázquez, M., & Smarandache, F. (forthcoming). Dynamic Epistemic Logic for Large Language Models. Neutrosophic Sets and Systems.

Neutrosophic Sets and Systems (open-access journal) — full archive at fs.unm.edu/NSS

Happy to share preprints with either of you if there is interest. Daniel — looking forward to seeing Doninha.

Best,
Maikel Leyva-Vázquez
Universidad Bolivariana del Ecuador
Editor-in-Chief, Neutrosophic Sets and Systems