{\huge Does Logic Apply To Hearings?}

The problem of mining text for implications

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 then, as one would expect, widely reported.

In real time, I heard Admiral Rogers's comments. Then I heard and read the reports about them. I am at best puzzled about what happened.

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 $latex {A}&fg=000000$ and later says $latex {A \implies B}&fg=000000$, can we conclude that he or she has effectively said $latex {B}&fg=000000$?

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 $latex {\forall x \in S \ A(x)}&fg=000000$ is true, then for any $latex {c}&fg=000000$ in the set $latex {S}&fg=000000$ it must follow that $latex {A(c)}&fg=000000$ is true.

Logic and Buffering

What is going on here? The reports that he refused to answer `is $latex {A(c)}&fg=000000$ true?' are correct. But he said a stronger statement in my mind that $latex {\forall x \in S \ A(x)}&fg=000000$ is true. Is it misleading reporting? Or do the rules of logic not apply to testimony before Senate committees? Which is a stronger statement:

$latex \displaystyle A(c) &fg=000000$

$latex \displaystyle (\forall x \in S) \ A(x), &fg=000000$

In mathematics the latter statement is stronger, but it appears not to be so in the real world. The statement $latex {A(c)}&fg=000000$ 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 ``$latex {\forall x \in S \ A(x)}&fg=000000$'' rather than ``$latex {A(c)}&fg=000000$'' 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

$latex \displaystyle (\forall x \in S)\mathit{HasWings}(x) \rightarrow \mathit{CanFly(x)}. &fg=000000$

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 $latex {X}&fg=000000$. In one place it states that $latex {X}&fg=000000$ occurred at time $latex {t}&fg=000000$ and occurred ``once again'' at time $latex {t'}&fg=000000$. The question is whether one can infer and apply the rule

$latex \displaystyle (\forall t,t',t'') (X(t) \wedge \mathit{OnceAgain}(X,t') \wedge t < t'' < t') \rightarrow \neg X(t''). &fg=000000$

Open Problems

How soon will we have apps that can take statements of the form $latex {(\forall x \in S)A(x)}&fg=000000$ and deduce $latex {A(c)}&fg=000000$ for a particular $latex {c \in S}&fg=000000$ that we want to know about? Will inferences from ``material implication'' be considered material in testimony?