core/docs/adr/ADR-0259-conditional-membership-fusion-band.md

ADR-0259 — Conditional-membership fusion band (Band v4-CM)

• Status: Proposed
• Date: 2026-07-23
• Relates to: ADR-0258 (Band v3-MEM — this is its scope-out #1), ADR-0257 (Band v2-EN — the connective grammar this band reuses), ADR-0256 (earned license), ADR-0201 (ROBDD keystone), ADR-0175/0199 (calibrated learning / arena)

1. Context

ADR-0258 §6.1 reserved conditional–membership fusion as a future band:

"If Socrates is a man then Socrates is mortal. Socrates is a man. Therefore Socrates is mortal."

Band v3-MEM refuses this — mixed_structure_out_of_band — because its per-sentence grammar treats a connective token (if/then/or/and/ either) anywhere in a sentence as announcing structure that band does not compose. Band v2-EN refuses the same text for the complementary reason: its opaque-atom minter explicitly rejects is [a|an] clauses (membership_shape_out_of_band) rather than flattening membership structure it cannot read. Each band is individually sound and, by design, refuses exactly what the other reads — the gap is the composition, not either reader's engine.

2. Decision

Add generate/proof_chain/cond_member.py — a third reader, tried strictly AFTER Bands v1 / v1b / v2-EN / v3-MEM (a fallback tier; every previously served argument stays byte-identical) — that composes v2-EN's connective grammar (if/then, or, and, either sugar, top-level and-splitting) with v3-MEM's singular membership sentence reading, over the SAME per-individual atom space:

• Sentence dispatch (closed, ordered): a bare top-level X and Y premise (no if/or anywhere) splits into independent singular records, exactly as v2-EN does — semantically conjoining, keeping the connective inventory the shape-bands classify over uncluttered. Any OTHER sentence containing a connective token is parsed by the ported junction/conditional grammar below. A universal-lead (all|every|each| no) sentence with NO connective token is a bare universal, read UNCHANGED by v3-MEM's own _parse_universal. Everything else is a bare singular fact, read UNCHANGED by v3-MEM's own _parse_singular (which already normalizes every negation form this band needs — leading not, the sentential it is not the case that prefix, and copular is not). Checking for a connective token BEFORE the universal-lead dispatch (not after) is load-bearing: it is what stops a connective token from ever silently leaking into an opaque name/class run.
• Connective grammar over membership leaves: if <A> then <B> and <A> or <B> / <A> and <B> (with either as sugar, mixed and+or at one level refused as ambiguous_and_or, a conditional nested inside another refused as nested_conditional — identical restrictions to v2-EN, ported verbatim) build a small formula tree (_Lit / _And / _Or / _Implies) whose LEAVES are v3-MEM singular facts, not opaque atoms. Because _parse_singular is negation-aware on its own, this band's grammar needs no separate negation layer — v2-EN needs one only because ITS leaf-miller (_AtomTable.mint) is negation-blind.
• A conclusion stays a single singular fact (optionally negated), matching v3-MEM's existing discipline exactly: a universal or connective-shaped conclusion refuses (universal_conclusion_out_of_band / new compound_conclusion_out_of_band) rather than attempting a compound render.
• One shared per-individual atom space: every singular fact — whether a bare sentence, an and-split part, or a leaf nested inside a connective tree — contributes to the SAME two-pass lowering v3-MEM already performs (collect named individuals and closed-morphology class-groups first, THEN mint one opaque atom per attested (individual, class) pair, THEN instantiate every bare universal at every named individual). A bare universal may now instantiate at an individual named ONLY inside a connective's leaf, and a connective's leaf atom may now UNIFY with an atom a bare universal's instantiation also produced — this atom-sharing across the two mechanisms is the fusion the band is named for, and nothing about it is a new soundness claim: it is the same per-individual instantiation ADR-0258 §3 already proved sound, applied to a strictly larger set of premise formulas.
• Four new shape-bands, priority order first-match: en_condmem_fused (a bare universal coexists with a connective sentence — the mechanism above genuinely fires), en_condmem_disjunctive (an or appears anywhere in any connective sentence), en_condmem_chain (two or more connective sentences, no universal, no or), en_condmem_conditional (the base case — exactly one if/then, no universal, no or). A successfully-decided argument in this band always contains at least one connective sentence — every other reason v3-MEM would refuse also makes THIS reader refuse identically (it reuses v3-MEM's own _parse_universal/_parse_singular, guards included), so there is no connective-free case this band could newly decide; no fifth "atomic" band is needed.

3. Why the composition is sound (the load-bearing argument)

1. Nothing here is a new inference rule. Every connective (&, |, ->) is standard propositional structure the ROBDD engine already decides; every leaf is a v3-MEM singular-membership atom, minted and linked by the IDENTICAL closed morphology relation ADR-0258 §3 already proved sound and (for this fragment) complete. Composing them is substitution of one sound reading's atoms into another sound reading's connective positions — the propositional engine's soundness does not care which reader supplied which formula string.
2. Universal instantiation stays sound when the instantiated individual is named only inside a connective. ADR-0258 §3's argument — every first-order model of ∀x(C1(x)→C2(x)) satisfies the instantiation at every domain element, so at every NAMED individual in particular — does not depend on WHERE in the argument that individual's name appears. An individual introduced solely as the subject of an if-clause leaf is still a named individual; instantiating a bare universal at it is still a sound consequence of the universal, exactly as if it had appeared in its own bare sentence.
3. Completeness is preserved for the same closed fragment. The fragment is unchanged from ADR-0258 (singular literals + A/E universals, Boolean reading, no existential import) with one syntactic widening: singular literals may now be combined by &/|/-> before appearing as a premise or antecedent/consequent. A propositional countermodel still lifts to a first-order countermodel over exactly the named individuals, by the identical argument — connectives among already-Boolean atoms do not change what "every element is a named individual" needs to guarantee. UNKNOWN therefore still means genuinely not forced within the disclosed reading, and the surface still scopes itself exactly as v3-MEM's does (reused verbatim — see §4).
4. The refusal vocabulary stays a strict superset of v3-MEM's, plus v2-EN's connective-shape guards. nested_conditional and ambiguous_and_or are v2-EN's own restrictions, ported unchanged (English and/or scope genuinely is ambiguous when mixed; a conditional nested inside another is refused rather than guessed at, in both bands identically). compound_conclusion_out_of_band is new and narrow: it exists only to keep the conclusion a single renderable fact, not to hide any inference.

4. What the earned licenses certify; rendering

Same posture as ADR-0258 §4: the license certifies reader fidelity, not engine soundness. render_entailment_member (ADR-0258) is reused UNCHANGED for this band's surface — its UNKNOWN scoping ("reading each name as one individual and each class word at face value…") is exactly as accurate here, since every clause in this band's arguments is read all the way down to individual+class; connectives introduce no additional hidden structure the surface would need to disclose. No new render function is added.

5. Scope-outs (deliberate)

1. A universal clause cannot be nested inside a connective — only a bare top-level universal sentence instantiates; if all men are mortal then … refuses (typed, via the same connective-shape-first dispatch that protects bare universals from silent corruption). Composing a QUANTIFIED antecedent/consequent is a larger, separate question (it would need bound-variable tracking across clauses, not just shared individuals) and is left for a future band if a real case ever needs it.
2. Existential premises, tense, verb predicates, identity/definite descriptions — unchanged scope-outs, inherited from ADR-0258 §6 via the reused _parse_singular/_parse_universal.
3. Flag posture unchanged: rides deduction_serving_enabled (default off); no new flag.

6. Verification

• uv run core test --suite deductive -q — reader contract, surfaces, license, all four lane splits, e2e through ChatRuntime.
• Practice arena: 17 bands × 720 = 12,240 cases, wrong=0 required for every band; ledger re-sealed (chat/data/deduction_serve_ledger.json).
• Eval lane: v1 28/28, v2_en 26/26, v2_member 26/26, v2_condmem new — wrong=0; report re-pinned (scripts/verify_lane_shas.py).