Romero's 2026 revision fixes a parenthesization-dependence flaw Gracia Di Rienzo (2025) found in Bunge's partial-truth axiomatization, by aggregating over a fixed elementary set instead of recursive pairwise averaging

philosophy-of-sciencepartial-truthformal-logicmario-bunge

Romero's paper is a targeted repair of Mario Bunge's own axiomatization of partial truth (Matter and Mind, 2010; "The correspondence theory of truth," Semiotica, 2012), prompted by a flaw Romero attributes to Agustín Gracia Di Rienzo's 2025 paper "On Bunge's axiomatizations of 'partial truth'" (Disputatio: Philosophical Research Bulletin 14, 175–184): "A recent analysis showed that a binary half-sum rule for conjunction can assign different values to logically equivalent expressions that differ only in their parenthesization." Under Bunge's old rule, V_E(p∧q) = (V_E(p)+V_E(q))/2 applied recursively, the grouping ((p∧q)∧r) implicitly weights the three components 1/4, 1/4, 1/2, while (p∧(q∧r)) weights them 1/2, 1/4, 1/4 — so, using the worked values V_E(p)=1, V_E(q)=0.5, V_E(r)=0, the two logically equivalent groupings compute to 0.375 and 0.625 respectively.

Romero's fix "address[es] that instance by abandoning recursive binary averaging and retaining component counts and weights correctly when combining disjoint groups": both groupings are instead evaluated from the identical elementary set {p, q, r}, and the paper reports both now reduce to (1 + 0.5 + 0)/3 = 0.5 regardless of parenthesization. The paper is explicit about the fix's scope — it is not a general numerical calculus for negation or disjunction, and the arithmetic-mean aggregation itself rests on flagged assumptions (comparability of component valuations, appropriateness of compensation between an inaccurate and an accurate component) rather than being forced by the mathematics alone. See claim-romero-2026-partial-truth-valuation-distinct-from-probability-verisimilitude for what V_E measures when applied to a single proposition.