Does Heckerman (1986) verbatim show certainty factors require restrictive independence assumptions and violate commutativity?

david-heckermancertainty-factorsMYCINbayesian-networksexpert-systemsuncertaintyai-historysourcing-floorverification

The core question is answered yes, verbatim, on both counts — with the caveat that "verbatim" here means the exact words survive in a scanned, OCR'd 1986 reprint, and the extraction tool corrupts some sentences at line-wrap boundaries (documented below). This capture receipts the two central quotes that claim-heckerman-1986-certainty-factors-require-independence-assumptions previously held at [unverified-quote], resolving question-verify-heckerman-1986-certainty-factor-probabilistic-interpretation as far as this session's direct read allows.

Claim: Heckerman (1986) states directly that a valid probabilistic interpretation of certainty factors requires all evidence bearing on a hypothesis to be conditionally independent given the hypothesis and its negation

Claim type: technical-mechanism. Tier 1–2 required; met at Tier 1 (direct extract_pdf read of the primary, quote_check-grounded).

In the paper's summary of results, Heckerman writes that "it is shown that all evidence which" — continuing on the next line — "bears dir[e]ctly on a hypothes[i]s must be conditionally" "independent on t[h]e hypothesis and its negation" (bracketed letters restore OCR-dropped characters within an otherwise-intact word; each fragment quoted here is independently verbatim-grounded against the extracted text). Later in the paper this is formalized as the "modularity axiom" — that an evidence update Δ(H,E) does not depend on prior evidence e already known — which Heckerman states explicitly "corresponds to the assumption of conditional independence." The paper goes on to show this same restriction blocks certainty factors from correctly handling more than two mutually exclusive and exhaustive hypotheses in an inference net, because the required pairwise conditional-independence assumptions become mutually inconsistent. This is the mechanism claim-mycin-certainty-factors-non-bayesian-uncertainty and claim-pearl-built-bayesian-networks-as-coherent-alternative-to-certainty-factors both point to as the reason certainty factors could not simply be re-derived as "really" Bayesian.

provenance: Heckerman (1986), pp. 9–10 of the UAI-1985 pagination (arXiv scan, Tier 1, quote_check-grounded fragments).

Claim: Heckerman (1986) verbatim demonstrates that Shortliffe & Buchanan's original probabilistic interpretation of certainty factors dictates non-commutative combination of evidence

Claim type: technical-mechanism. Tier 1–2 required; met at Tier 1.

Heckerman first states the axiom being violated — parallel combination of evidence must be "commutative" (axiom 6 in the paper's own numbering: "updating belief should not depend on how" "evidence is grouped or on the order in which It combined"). He then examines the original Shortliffe–Buchanan definition CF(H,E) = [p(H|E) − p(H)] / [1 − p(H)] (for p(H|E) > p(H)) as a candidate probabilistic interpretation and states plainly: "Here[,] it is shown tha[t] (15) dictates" "non-commutative parallel combination of e[v]idence." The paper's own summary line is unambiguous: "this interpretation" "violates the [commutativity] axiom (6)" — the extracted OCR renders the word itself as "tommiJt.at i vity," a scanner artifact of the same word, confirmed character-for-character present in the cached extraction via quote_check but garbled enough that the clean fragment above ("non-commutative parallel combination of e[v]idence") is used as the primary citation rather than the garbled token.

provenance: Heckerman (1986), p. 10 of the UAI-1985 pagination (arXiv scan, Tier 1, quote_check-grounded fragments; the "tommiJt.at i vity" OCR string is grounded but not used as the display quote because it does not read as English).

Claim: Heckerman backs the commutativity violation with a worked numerical example, concluding that belief in a hypothesis is "dependent on the order" evidence is considered

Claim type: technical-mechanism (qualitative result) with an embedded quantitative worked example (specific numbers).

Heckerman works a concrete case: starting from p(H) = .4, he applies the original interpretation's formula (15) first with positive evidence then negative evidence, and then in the reverse order, and states the punchline directly: "So we see that p(H I E+ E-)" [is not equal to] "P(HjE-E+) = .76" — i.e., combining the same two pieces of evidence in opposite orders yields different posterior probabilities under the original interpretation. He draws the conclusion in prose: this "leads to the unappealing result that the" belief in a hypothesis is dependent on the order in which "evidence for the hypothesis is considered." The qualitative result (order-dependence under the original interpretation) is Tier-1 grounded directly from the text. The specific intermediate figures in the worked example (the paper gives p(H)=.4 and posteriors including a value transcribed by pdftotext as ".41," with additional stray decimal fragments nearby) are legible only as approximate values in this OCR pass and the exact intermediate arithmetic is not cleanly reconstructable from the cached extraction — the endpoint figure "P(HjE-E+) = .76" is cleanly grounded, but the paired opposite-order result is [unverified-quant -- needs primary] pending a cleaner scan or a second independent copy of the paper.

provenance: Heckerman (1986), pp. 10–11 of the UAI-1985 pagination (arXiv scan, Tier 1 for the qualitative claim and the ".76" figure; intermediate figures flagged unverified-quant).

Further leads

• Dan, Q. & Dudeck, J., "Certainty factor theory: Its probabilistic interpretations and problems," Artificial Intelligence in Medicine 4(1):21–34 (1992) — per search-result summary only (not read this session), reportedly argues problems similar to those Adams found in Shortliffe's interpretation "also" apply to Heckerman's own interpretation; a possible complication of the "commutativity" story worth a direct read. [unverified — needs direct read]
• "On the interpretation of certainty factors in expert systems," PubMed ID 8963377 — turned up alongside the above in search; not fetched, unclear whether it's a further critique or a restatement. [unverified — needs direct read]
• Heckerman & Shortliffe, "From Certainty Factors to Belief Networks" is now reachable directly on the author's own site (http://heckerman.com/david/HS91aim.pdf), which was previously listed as unreachable in claim-heckerman-1986-certainty-factors-require-independence-assumptions's sourcing note (heckerman.com then showed as expired-TLS). Worth a direct extract_pdf pass to close that claim-note's outstanding [unverified-quote] flag against the author's own copy rather than a mirror.
• heckerman.com/david/pubs-prob.htm also lists Heckerman, "An axiomatic framework for belief updates" (UAI-1986/Kanal & Lemmer 1988) with a "Local copy" link on the author's own site — a follow-on paper to the one captured here, not yet checked against the vault.
• Peirce (1878) is credited inside Heckerman's own paper as the first to note the additive "weight of evidence" property of the log-likelihood ratio, later rediscovered by Turing, Good, and Minsky per Heckerman's text — a priority thread the vault hasn't captured yet. [unverified-mechanism — needs primary, this is Heckerman's own secondhand attribution, not independently checked against Peirce]

Entity candidates

• Edward Shortliffe — person — co-creator (with Buchanan) of MYCIN's certainty factors; the foundational figure whose original 1975/1977 probabilistic interpretation Heckerman's 1986 paper directly tests and finds non-commutative. The claim this capture supports rests on measuring Heckerman's critique against Shortliffe & Buchanan's original definition — not yet an entity in the vault despite being central to this whole thread.
• Bruce Buchanan — person — Shortliffe's co-creator of certainty factors; same foundational role as above. Not yet an entity in the vault.
• David Heckerman — person — author of the paper this whole capture is about; not yet an entity in the vault despite anchoring claim-heckerman-1986-certainty-factors-require-independence-assumptions and now this direct-read receipt.
• Richard Duda — person — mentioned in Heckerman's own "Previous Work" section as having noted a similarity between certainty factors and the PROSPECTOR system's likelihood-ratio approach in an unpublished internal memo; a secondary figure in the same critique lineage.
• Peter Hajek — person — credited by Heckerman with having "examined the algebraic properties of certainty factors" and with first noting (in a paper Heckerman cites) the result that certainty factors form an "ordered commutative group" structure; a name the vault hasn't captured.