Friday, May 11, 2007

Joseph Laronge Demonstrates How to Use Rationale to Portray a Witness Credibility Problem

The following illustration is found on Joseph Laronge's blog Inference Path:

The example is not trivial: witness credibility is perhaps the most complex inference problem known to ordinary human mortals. (I say "ordinary" to put to one side esoteric problems such as string theory and quantum computing.)

Laronge's mode of visualizing credibility problems seems analytically correct and makes it possible in Rationale readily to marshal evidence bearing on distinct credibility attributes, or variables. (Peripheral note: I would add to the list of variables; I would include, e.g., objectivity vel non and ability to communicate [or use language] vel non.)

Thursday, May 10, 2007

The Impossibility Principle

Lotfi Zadeh, Extended Abstract, From Fuzzy Logic to Extended Fuzzy Logic—The Concept of F-validity and the Impossibility Principle, Lecture given at FUZZ-IEEE 2007, Imperial College, London, UK:
In an environment of imprecision, uncertainty, incompleteness of information, conflicting goals and partiality of truth, p-validity [provable validity; a provably valid solution] is not, in general, an achievable objective.
It does not follow, of course, Zadeh asserts, that logic dissolves into incoherence. Instead, logic becomes fuzzy -- in the extended sense that Zadeh describes in this lecture and on other occasions and in other publications.

The conception is bold. I am not a logician. But I would hesitate to dismiss Zadeh's (attempt at) radical (re)conceptualization of logic. Zadeh has grounds for making the following assertion (id.):

Fuzzy logic has come of age.
He adds:
During much of its early history, fuzzy logic has been an object of skepticism and derision, in part because fuzzy is a word which is usually used in a pejorative sense. Today, fuzzy logic is used in a wide variety of products and systems ranging from cameras, home appliances, medical instrumentation and automobiles to elevators, industrial control, subways, fraud detection and traffic control systems.
Whether or not fuzzy logic makes sense and whether or not it "works," Zadeh is plainly right in saying and complaining:
[T]here are still many misconceptions about fuzzy logic. To begin with, fuzzy logic is not fuzzy. Basically, fuzzy logic is a precise logic of imprecision.
Furthermore, there is more to fuzzy logic, he rightly adds, than the concept of a fuzzy set. However, for want of technical proficiency, I will not even begin to try to recount or summarize Zadeh's account of the four principal facets of fuzzy logic. Instead, I limit myself to quoting this statement:
More specifically, in fuzzy logic everything is or is allowed to be graduated, that is, be a matter of degree or, equivalently, fuzzy. Furthermore, in fuzzy logic everything is or is allowed to be granulated, with a granule being a clump of attribute values drawn together by indistinguishability, equivalence, similarity, proximity or functionality.
What does this mean? The answer cannot be simple. My intuitions are too poor to help me out here.

Zadeh proceeds to talk about natural language and he asserts (as he has done before) that "a natural language is viewed as a system for describing perceptions." He then proceeds to describe a program for the development of a logic or -- more precisely stated -- "a maximally expressive constraint definition language" that can "serve as a meaning representation/precisiation language for natural languages."

It is intriguing and revealing that Zadeh views the ability to use computations to mimic or manipulate (natural) words as almost equivalent to, or very closely related to, the ability to interpret perceptions:

Since a natural language is a system for describing perceptions, NL-Computation is closely related to computation with perception-based information. NL-capability is the capability of a theory to operate on information described in natural language or, equivalently, to operate on perception-based information. The importance of NL-capability derives from the fact that much of human knowledge is expressed in natural language.
The last sentence in the above quotation bears emphasis: Zadeh asserts (correctly, I think) that much genuine human knowledge is embedded in, or carried by, ordinary words [natural language].

Zadeh, as before, does not hesitate to embrace inference rules that look very different from the sorts of inference rules we are accustomed to seeing in traditional deductive and traditional if-then logic -- but, note, Zadeh refuses to cede any ground to traditional bivalent logic and insists on calling his new inference rules rules for drawing deductions:

Deduction in fuzzy logic is governed by a collection of rules of deduction which, in the main, are rules that govern propagation and counterpropagation of generalized constraints. The principal rule is the extension principle. Extension principle has many versions. The simplest version (Zadeh 1965) is the following. Let f be a function from reals to reals, Y=f(X). What we know is that X is A, where A is a fuzzy subset of the real line. Equivalently, what we know about X is its granular value, that is, its possibility distribution, A. What can be said about Y, that is, what is its granular value or, equivalently, its possibility distribution? In a more general form, (Zadeh 1975) X is A is replaced by f(X) is A. It is this form that is used in most practical applications. In a form that is used in fuzzy control, what is granulated is f, resulting in a granular function, f*, which is defined by a collection of fuzzy-if-then rules. More generally, the extension principle may be viewed as follows. Let Z =f(X), where X is a real-valued variable. Assume that we can compute Z for singular values of f and X. Basically, the extension principle serves to extend the definition of Z to granular values of f and X.
What does this all mean -- precisely? I am the wrong person to ask.

But to the eyes of this amateur, this ingenue, and this reckless autodidact, Zadeh's theory strikes me as one that must be taken very, very seriously.

In any event(!): There are delicious observations in Zadeh's abstract. For example:

Turning to Case 2, we observe that, in general, precision carries a cost.
This point is -- in some sense -- indubitably correct. In what sense? Well then, read Zadeh and then think about the question. And then -- and only then -- render your opinion.

Zadeh does not claim that he has already developed the broad sort of fuzzy logic that he thinks is required. He writes:

The concepts of extended fuzzy logic, FL+, and f-validity which are sketched in the following represent a more radical development. In essence, extended fuzzy logic may be viewed as an attempt at legitimizing the concept of fuzzy theorem (Zadeh 1975) and fuzzy validity. In large measure, the move from fuzzy logic, FL, to extended fuzzy logic, FL+, is a move into as yet uncharted territory.
Zadeh does not hesitate to stare directly at the seemingly anomalous, or paradoxical, character of the sort of logic he yearns to develop and justify:
A conclusion which is of key importance is that there are no crisp theorems in f-geometry.
There are no crisp arguments! What a baffling, strange, and intriguing proposition!
  • But, of course, lawyers are thoroughly familiar with this strange proposition: none of their arguments are "crisp." But they are full of arguments. And many lawyers even think that their arguments are arguments. They should therefore -- by all rights -- read Zadeh. There they will find a stout defender of their craft and of law's peculiar logic.
  • Looking Up Down Under


    In 2008 I will be a visitor down under: for part of my sabbatical leave (February and March) I will be a visiting professor at the University of New South Wales Faculty of Law. (I am to be the Julius Stone Visiting Professor. More about the influential, interesting, and prolific Julius Stone later.)

    I have many reasons for looking forward to this visit. Among my reasons is the presence of many interesting people down under -- for example, the mathematician, historian, and social commentator James Franklin at the University of New South Wales, Tim van Gelder in Melbourne, and many other people, people I hope to mention and discuss on these pages later.

    But one of my reasons for looking forward to my visit down under is looking up -- looking up at the skies, that is. There are few places on earth with little "light pollution." Death Valley in California was once such a place. But many parts of Australia are an astronomer's paradise -- dry air and little man-made light.

    It has been decades since I was an active amateur astronomer. But I hope to pick up this avocation again a little bit when I go to Australia. The opportunity to go to regions where the skies are truly dark, much the way they were thousands of years ago, is just too alluring to resist.

    Now I have to buy some good astronomical binoculars (nothing more fancy). I am terribly behind the times. I loved my small refractor, crude and misshapen though it was. Now, for about the same amount of money, I will get a far better device, one that will partially remedy the ravages of time on my eyes.

    N.B. I hope to visit Tasmania -- to look down at marsupials and other terrestrial wonders.

    Gemini Observatory, US National Science Foundation, and the University of Hawaii Institute for Astronomy

    Tuesday, May 08, 2007

    James Fallows in Atlantic on Tim van Gelder's Rationale

    Computer-assisted critical thinking has become the soup du jour -- and, one hopes, the flavor of the year -- in the (some) mass media. See James Fallows, What Was I Thinking?, in The Atlantic pp. 131-133 (June 2007):
    This leads to the newest ambitious entry: Rationale, an “argument processor” from a start-up company in Melbourne, Australia, called Austhink. The firm’s CEO, Tim van Gelder, is a former academic philosopher whose specialty was teaching critical thinking—that is, preparing students to examine the premises of any argument, another person’s or their own. He had a discouraging experience in the 1990s when teaching such classes at universities in the United States. “Despite my best efforts, and maybe theirs, it just wasn’t working,” he told me in a Skype conversation, he in Melbourne and I in Shanghai. He was gracious enough not to attribute this failure to the defects of America’s K-12 school system. Instead, he concluded that people in general needed better training in assessing arguments. After returning to Australia, he raised money to start a company and create a program that could be used by schools for teaching logic.

    In operation, the Rationale program is quite simple. You state a main contention you are trying to test—I should buy a new house, we should invade Iran—and then systematically list each of the supporting claims for it. Then you list the objections to each claim, and the rebuttals to those objections, and so on until you’re down to first principles—all of which are shown as connected boxes on a map. “To the extent you are perfectly clear about your thoughts, this should be a trivial process,” van Gelder told me. But in reality, he said, people find it more challenging than they expect, and this visual representation of the claims and counterclaims generally provokes a new perspective on the ideas at stake.

    The more factors there are to weigh in making a decision—and, especially, the more views there are to reconcile when more than one person is involved in a choice—the more helpful this logic map can be. For example, a “tree” view in Rationale can show the full chain of assumptions that lead to a particular conclusion, which in turn helps identify exactly where people with different views disagree. “Everyone knows that complex structure is generally more easily understood and conveyed in visual or diagrammatic form,” van Gelder wrote in an academic paper. “That is why, for example, we have street maps rather than verbal descriptions of the layout of cities.” The same principle applies in complex debates, he told me, because in all but the simplest discussions people have a hard time remembering all the relevant considerations.

    Van Gelder’s initial sales target was schools and universities, but he increasingly sells to consulting firms, govern‑ ment agencies, and other groups wrestling with decisions, as well as to individuals. The strongest interest has come from U.S. intelligence agencies, which are using the software to train analysts to think critically about intelligence claims. I was gracious enough not to ask van Gelder why he didn’t finish the program a few years earlier.

    Probability in Science and (Religious) Faith

    Probability theory and one of my little books have been enlisted (on the side of God, against Richard Dawkins) by an Oxford don (at Cambridge University) in the recent wars over the tension between faith and science. See Alister McGrath, Has Science Eliminated God? Richard Dawkins and the Meaning of Life (Lecture, 2004). See, in particular, note 23, citing P. Tillers & E. Green, PROBABILITY AND INFERENCE IN THE LAW OF EVIDENCE: The Uses and Limits of Bayesianism (1988).
  • I will forgive Professor McGrath -- it's the Christian thing to do -- for listing Eric Green as the lead editor. (Eric and I negotiated this matter when this matter mattered.)

    I confess that I am pleased that Professor McGrath took note of my little book (despite Professor McGrath's failure to note the proper order of the editors): it's nice to know that someone thinks that debates about probability touch the deepest questions of life.

    The connection between theological debate and probability theory is not new. See, inter alia, Blaise Pascal (again, betting on God rather than non-God).

  • Can't We All Get Along?

    R.R. Reno, Moses and Multiculturalism, First Things (May 7, 2007):
    [Martha] Nussbaum sounds like Rodney King with subordinate clauses. [In Cultivating Humanity: A Classical Defense of Reform in Liberal Education] [s]he hopes for a university dedicated to “cross-cultural understanding” and “respectful dialogue” that will produce an environment “in which we can all learn to function as citizens of the entire world.”
    The stiletto is sharp and clever. Withal, Professor Nussbaum's faith in the humanizing properties of higher education is touching (in the good sense). But one naturally wonders if Nussbaum's faith is factually warranted. Much depends, of course, on what the university actually looks like. There is a difficulty: one wants unvarnished discussion and debate rather than propaganda (however well-intended). One also wants "good values." What kind of university generates them? At what price?

    Monday, May 07, 2007

    Rationale redux

    The folks at Austhink have been busy and they have created another wiki illustrating how law might be made Rationale. This time they created an even richer tapestry:

    Rationale Law

    Tim van Gelder has created a wiki illustrating the use of Rationale (software) to portray reasoning about a legal problem. Here is the colorful picture that he developed:

    Sunday, May 06, 2007

    Ellis Island, May 6, 2007


    My family and I (all three of us) arrived, not at Ellis Island (which you see here), but at the Brooklyn docks, which you do not see here, but which lay (they no longer exist) across the Hudson River (which you see in this view) and, beyond that, past Manhattan and then across the East River.

    Posted by Picasa

    Jersey City-New York City Renaissance

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    Liberty Park Walkway, May 6, 2007

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    Lay Judges and Common Sense to Arrive in Japan in 2009

    Kyodo News, Lay judges to be advised to use "common sense", in Japan Times Online (May 6, 2007):
    The presiding professional judge in the incoming citizen judge system will tell the lay participants to use their "common sense" in deciding criminal cases, according to draft models of such instructions.

    The models map out what presiding judges are expected to tell the lay judges, who will be randomly chosen from the general public, before they begin examining criminal cases under the system taking effect in 2009.

    Among the phrases recommended are "Make a judgment in accordance with your common sense solely on the basis of evidence presented to the court," ... "Your opinion has the same weight as that of a (professional) judge," and "You are allowed to talk to others about (general) impressions you formed by serving (as a lay judge)."


    The top court is expected to lay out some basic legal concepts, such as "who shoulders the burden of proof" and "evidence-based examinations," while allowing individual courts to decide what precisely to tell lay judges.Under the new trial system, six eligible voters selected as lay judges will hear murder and other serious criminal cases with three professional judges at the first court of instance, working with them in reaching a verdict, and in the case of a guilty ruling what kind of sentence to hand down.

    Under the draft models, lay judges will be briefed on some ground rules at the beginning of a trial, such as how the trial will proceed and what they should base their judgments on.

    Specifically, they will be asked to give a guilty verdict if they have concluded that prosecutors' evidence is correct and give a not-guilty verdict if prosecutors cannot prove a defendant's guilt beyond reasonable doubt.

    They will be advised to exercise their common sense and to express their opinions, with an understanding that their opinions weigh as much as those of the professional judges.

    The lay judges will be warned not to divulge details of the discussions among judges, so they can "exchange candid opinions" and "protect their own safety," according to the models.


    The three professional judges and the six lay judges will make decisions by majority. However, no guilty sentence will be handed down if all three professional judges find the accused innocent.