The problem of mining text for implications

 2016 RSA Conference bio, speech

Michael Rogers, the head of the National Security Agency, testified before the Senate Intelligence Committee the other day about President Donald Trump. He was jointed by other heads of other intelligence agencies who also testified. Their comments were, as one would expect, widely reported.

The various reports all were similar to this:

Adm. Michael S. Rogers, the head of the National Security Agency, also declined to comment on earlier reports that Mr. Trump had asked him to deny possible evidence of collusion between Mr. Trump’s associates and Russian officials. He said he would not discuss specific interactions with the president.

## Why I Am Puzzled

The above quote is accurate—Adm. Rogers did not discuss specific interactions with the president. But I have trouble with this statement. The problem I have is this:

Are statements made in a Senate hearing subject to the basic rules of logic?

For example, if a person says ${A}$ and later says ${A \implies B}$, can we conclude that he or she has effectively said ${B}$?

Let’s look at the testimony of Adm Rogers. He insisted that he could not recall being pressured to act inappropriately in his almost three years in the post. “I have never been directed to do anything I believe to be illegal, immoral, unethical or inappropriate,” he said.

During his three years as head of the NSA he worked under President Obama and now President Trump. So I see the following logical argument. Since he has never been asked to do anything wrong during that period, then it follows that Trump never asked him to do anything wrong.

This follows from the rule called universal specification or universal elimination. If ${\forall x \in S \ A(x)}$ is true, then for any ${c}$ in the set ${S}$ it must follow that ${A(c)}$ is true.

## Logic and Buffering

What is going on here? The reports that he refused to answer ‘is ${A(c)}$ true?’ are correct. But he said a stronger statement in my mind that ${\forall x \in S \ A(x)}$ is true. Is it misleading reporting? Or do the rules of logic not apply to testimony before Senate committees? Which is a stronger statement:

$\displaystyle A(c)$

or

$\displaystyle (\forall x \in S) \ A(x),$

where ${c}$ is an element of ${S}$?

In mathematics the latter statement is stronger, but it appears not to be so in the real world. The statement ${A(c)}$ is more direct. What does this say about logic and its role in human discourse?

Ken recalls a course he took in 1979 from the late Manfred Halpern, a professor of politics at Princeton. Titled “Personal and Political Transformation,” the course used a set of notes that became Halpern’s posthumous magnum opus.

The notes asserted that components of human relationships can be classed into eight basic modalities, the first three being paradigms for life: emanation, incoherence, transformation, isolation, subjection, direct bargaining, boundary management, and buffering. The first three form a progression exemplified by Dorothy and the wizard vis-à-vis Glinda and the ruby slippers in The Wizard of Oz; later he added deformation as a ninth mode and fourth paradigm and second progression endpoint. It particularly struck Ken that presenting mathematical proofs is classed as a form of subjection: You can’t argue or bargain with a proof or counterexample.

Buffering made and remained in his list. He showed how each member is archetypal in human history and depth psychology. So Ken’s answer is that the one-step-remove of saying “${\forall x \in S \ A(x)}$” rather than “${A(c)}$” is a deeply rooted difference. It makes wiggle-room that a jury of peers might credit in a pinch.

## Mining Logical Inferences

Psychology aside, the mining of logical inferences is a major application area. Sometimes the inference is outside the text being analyzed, such as when “chatter” is evaluated to tell how far it may imply terrorist threats. We are interested in cases where the deduction is more inside. For instance, consider this example in a 2016 article on the work of Douglas Lenat:

A bat has wings. Because it has wings, a bat can fly. Because a bat can fly, it can travel from place to place.

One might say that underlying this is the logical rule

$\displaystyle (\forall x \in S)\mathit{HasWings}(x) \rightarrow \mathit{CanFly(x)}.$

One of the problems, however, is that even if we limit the set ${S}$ to animals, the rule is false—there are many flightless birds. This leads into the whole area of non-monotonic logic which is a topic for another day—but good to bear in mind when revelations from hearings revise previously-held beliefs.

Ken has been dealing this week with an example at the juncture of the logic of time and human language. He had to evaluate twenty pages of testimony about a recurring behavior ${X}$. In one place it states that ${X}$ occurred at time ${t}$ and occurred “once again” at time ${t'}$. The question is whether one can infer and apply the rule

$\displaystyle (\forall t,t',t'') (X(t) \wedge \mathit{OnceAgain}(X,t') \wedge t < t'' < t') \rightarrow \neg X(t'').$

This was complicated by the document having been translated from a foreign language. Whether time ${t'}$ was the next occurrence of ${X}$ after time ${t}$ makes a difference to results Ken might give. Of course this may be clarified in a further round of testimony—but we could say the same about Admiral Rogers, and he has left the stand.

## Open Problems

How soon will we have apps that can take statements of the form ${(\forall x \in S)A(x)}$ and deduce ${A(c)}$ for a particular ${c \in S}$ that we want to know about? Will inferences from “material implication” be considered material in testimony?

Update, 11:15pm 6/8/17: CNN has just told of a woman they interviewed about the contradictions between Donald Trump and James Comey. Asked if she believes Comey lied, she replied, “No.” Asked if she believes Trump lied, she replied, “No.” Asked how that could be, she said: “The media has distorted it.” Thus the logical law of excluded middle is replaced by a “law of occluded media,” which blocks constructive inference…

1. June 8, 2017 4:32 pm

From Rudy Rucker:
The Marx brothers are in a room, and Zeppo says, “We’ve to think!” Chico replies, “Nah, we already tried that.” ha ha

The universal affirmatives, or A-propositions, are not adequate to to handle arguments in syllogistic reasoning that involve relations between pairs of things. In general, logic mostly allows us to follow our otherwise reasonable assumptions to contradiction in order to discover features we would otherwise have missed. Although a compelling feature in our world, the power of logic does not imply that the world itself is logical.

The second of my three favorite tautologies:

Modus tollens (~B & (A->B)) -> ~A
If the world were logical, then the world would make sense, but the world doesn’t make sense, so the world isn’t logical.

2. June 8, 2017 4:55 pm

Go Ask Alice, I Think She’ll Know …

Joining the Herrings already in Digress …

3. June 8, 2017 5:00 pm

Cf. Modus Dolens

4. June 8, 2017 5:08 pm

I think this may be related to the rubric of the ω-inconsistent mother.described by Paul Halmos.

5. June 8, 2017 6:30 pm

The purpose of these sorts of examinations is to discover how consistently the subject himself actually believes the things he has already answered.

“… and I’m never — never — sick at sea!”
“What, never?”
“No, never!”
“What, **NEVER**?”
“Well… Hardly Ever…”

Because people have been known to lie. So, that should be sufficient explanation for why an honest and logical senator would press from the general to the specific (if that’s what happened). And Editorial can react to the quotable quotes any way they like.

June 8, 2017 11:47 pm

> “I have never been DIRECTED to do anything I believe to be illegal, immoral, unethical or inappropriate,” he said… then it follows that Trump never ASKED him to do anything wrong.

No, it follows that Trump never DIRECTED him to…

7. June 9, 2017 9:09 am

Excellent point, Acct—thanks. Now here is a relevant juncture of Comey’s testimony yesterday:

[Senator James] RISCH: He [Trump] said, “I hope.” Now … Do you know of any case where a person has been charged for obstruction of justice or, for that matter, any other criminal offense, where they said or thought they hoped for an outcome?

COMEY: I don’t know well enough to answer. The reason I keep saying his words is I took it as a direction.

[and further exchange on “hope” versus “direction”]

We tried to keep logic and semantic aspects separate in the post; the logic is still a reason this should be followed up.

8. June 9, 2017 9:24 am

And then there is this, on how a question can be a command:

http://time.com/4811148/comey-testimony-henry-ii-thomas-becket-will-no-one-rid-me-of-this-meddlesome-priest/

9. June 9, 2017 10:27 am

a theme/ topic somewhat covered in gores book “the assault on reason”. human reason is based on the scientific revolution which is a bit tattered these days. reason is something that is not innate to humans, exactly. there is a sort of “psychological reasoning” that is not the same as mathematical logic. theres quite a bit of study of this in psychology, and esp in behavioral economics. there is james old quote, “a great many ppl think they are thinking when they are merely rearranging their prejudices”. how about, “reality has a liberal bias”? there are so many political quotes that show reason is somewhat of a auxiliary/ superfluous aspect at times. how about looking at wikipedias “list of logical fallacies”. its too bad this stuff isnt really taught in schools any more. if you ask me, reason is much of what separates humans from animals. its also found in neurobiology that its more of an attribute of the neocortex which is not fully developed in humans even up into their mid20s (that is relatively new research). amazing! re current state of science see also https://vzn1.wordpress.com/2017/04/27/tribute-to-science-2017-shifting-shearing-maybe-a-crossroads/

10. June 10, 2017 11:36 am