Non-Injective Truth Evaluation: The Sign-Erasure Fallacy in Classical Conditionals and Counterpossibles A Multiplicative Tri-Valued Relevance Calculus over {+1, −1, 0}

In elementary arithmetic, inferring 1 = −1 from the identities 1×1 = 1 and (−1)×(−1) =1 is a standard fallacy because squaring is a non-injective operation that erases inputsign polarity. This paper demonstrates that classical truth-functional logic and standardpossible-worlds counterfactual semantics commit an isomorphic structural error—termedthe Sign-Erasure Fallacy—when evaluating conditional propositions. By compressingboth grounded truth preservation (T → T) and double-falsehood vacuity (F → F) intoan indistinguishable monolithic output value (True), classical material implication erasesthe epistemic and ontological polarity of its inputs. While David Lewis’s possible-worldssemantics avoids this collapse for contingent falsehoods, it reproduces the exact samenon-injective erasure across counterpossibles (conditionals with impossible antecedents),certifying arbitrary pairs of impossibilities as trivially true. Conversely, unrelated true-to-true conditionals generate unearned redundancy without inferential connection. To resolvethis dual asymmetry, we formalize a Tri-Valued Philosophical Logic Calculus overthe polarity domain V = {+1, −1, 0} integrated with an objective HyperintensionalRelevance Filter RK(A, B) ∈ {0, 1}, governed by the unified multiplicative valuation ruleV (A ⇒ B) = vΦ(A) × RK(A, B) × vΦ(B). Under this operator, only inferentially connectedtruth pairings (+1, 1, +1) and coherent counterfactual dependencies (−1, 1, −1) yield Truth(+1), refuted claims (+1, 1, −1) and causal inversions (−1, 1, +1) yield Falsity (−1), andany irrelevant pairing (RK = 0) or impossible/empty component (vΦ = 0) halts evaluationat No Conclusion / Unknown (0).Keywords: Sign-Erasure Fallacy; Counterpossibles; Three-Valued Logic; HyperintensionalRelevance; Material Implication; Non-Injective Truth Valuation; Impossible Worlds; VacuousTruth.MSC 2020: 03B50 (Many-valued logic); 03B45 (Modal logic); 03B65 (Logic of naturallanguages).