First, in the analysis mode _Rationale_ does not allow

 "generation skipping" links between the propositions in "support"
boxes and the supported proposition.

Thus, this is permissible:

T

/\
 |
 |

X

But this is not permissible:

Z   <--------
                    |
/\                  |
 |                  |
 |                  |
                    |
T                  |
                    |
/\                  |
 |                  |
 |                  |
                    |
X  ------------

I assume that illegality of the second form stems from the view that
the stuff in lower level boxes function as premises, or reasons, for
the stuff in higher-level boxes.

But I am not sure - indeed, I do not believe - that generation-
skipping links should be outlawed when we are dealing with abductive
or inductive (rather than deductive) links, or connections.

Example: if X = "my son was home at the time of the crime"; T =
location of defendant at time of crime, and Z = the criminal guilt of
the son of the declarant of X. The assertion X may be directly linked
to Z as well as to T. (In this particular example the declarant if
more likely to lie if the criminal guilt of his son is in question. To
make the inference more intuitive, reverse the direction of the arcs.)

If one views X, T, and Z as propositions about states of the world, it
is not clear that X and T function as reasons. In any event Schum
believes and maintains, that there must be ancillary reasons (perhaps
"generalizations") that license or support the move from an X to a T
or from an X to a Z.

Whatever one thinks of Schum's thesis, I want, need, and must have a
diagramming grammar that allows generation-skipping links (and also --
by the way -- links between propositions that Rationale views as co-
premises for an upper level proposition or inference).

Of course, I can do some of what I want by using Rationale's
"Grouping" mode [or, given the questions that follow, can I?]  - but
if I take _Rationale_ into the Grouping mode (i) do I lose the ability
to make my arcs directed, (ii) do I lose my ability to bring parts of
the group into the foreground and make other parts recede into the
background, and (iii) and do I have or not have the ability to forge
lateral links among boxes at the same level in a tree? And where would
I then put Schum's ancillary propositions? (Sschum thinks of his
diagramming strategy as allowing a network to be embedded in a
network. That's not a bad way to think of what he's doing. Then, of
course, there is, in principle, no end to embedding; one stops when
one thinks it is appropriate or necessary.)

Peter: Could you make a Rationale diagram and augment it using a paint
program to make even clearer what you have in mind
for your application?

* * *

At present Rationale "maps" are of two diagrammatic types:

1. Trees: Grouping and Reasoning
2. A type of Hi-Tree: Analysis

Both of these structures are strictly hierarchical.  I.e. Every box
may have many children, but at most one parent.

Theoretically, for inter-generational links, what is needed is a graph
or network structure.
This might be accomplished by either:
    a. Adding additional links (non-hierarchical links)
    b. Going over to a directed "graph" (also called network)
structure in which instead of parent and children each
       box has 0 or more incoming and out-going edges.

What distinguishes these two approaches is that in the first case you
treat some links (the hierarchical ones) as more significant than the
others, whereas in the second case all links are of similar status
(although there are generalizations in which "weight" is a settable
property of links).

For an example of a generation-skipping link, see Figure 8 and the
accompanying text in my paper "Picturing Factual Inference in Legal
Settings," available at http://tillers.net/pictures/picturing.html,
and available in hard copy form in GERECHTIGKEITSWISSENSCHAFT:
Kolloquium aus Anlass des 70. Geburtstages von Lothar Philipps
(B. Schünemann, M.-Th. Tinnefeld, R. Wittmann, eds.; Berlin, 2005)

In another place I discuss another form of linkage not allowed by
_Rationale_: intra-generational links, links among propositions that
_Rationale_ views as co-premises. See Figures 8 & 9 and the
accompanying text in the online lecture "Probability and Uncertainty
in Law" (delivered in Konstanz in 2003), http://tillers.net/uncertainlaw/uncertain.html

You are all free to reconstruct, e.g., Figure 9. But I confess I would
be sad if you did: I think my Figure 9 is quite charming, quite
elegant. Why get rid of a good thing?

Peter T

On May 20, 6:08 pm, hydrof...@comcast.net wrote:

Two workarounds for Rationale.  First, we could just copy E so it was
in two places, preserving the tree structure. This happens a lot with
decision tree models. (Leading to decision graphs, where branches
leading to the same outcome can be fused.) Or, second, we could try to
partition E more finely to say *this* part of E supports I1, and
*that* part supports I2.

And of course, in the generation-skipping case, E might support H
directly, over and above the indicators. A common example from the
philosophy of causation is oral contraceptives and thrombosis. Oral
contraceptives (a) directly raise the chance of thrombosis, because
they partially mimic pregnancy, and pregnancy is a strong risk for
thrombosis. However, they also (obviously) reduce the risk of
pregnancy, thereby reducing the risk of thrombosis.  So we have:  C ->
P -> T and also C -> T,  using the arrows to show direction of
causation. For a probabilistic model, we need to capture the multiple
paths.

We could make it non generation-skipping by adding a dummy node, so we
have (a) C -> P -> T, and (b) C -> D -> T.  But we still have a
diamond structure. If we're not doing probabilistic inference, we can
just duplicate C, and have C -> P -> T <- C.

Obviously in Peter T's <a href="http://tillers.net/uncertainlaw/
uncertain_files/Figure_8_img.gif">Figure 8</a>, that would be a lot of
duplication. The question is whether ARGUMENT MAPS have to capture the
same complexities that a probabilistic inference model does. Joseph L.
has argued that tree structures are already hard to teach and convey
in the courtroom, so I think we need a more compelling concrete
example before pushing for complexity.

You make several pertinent points.

Naturally, we at Austhink are aware of the full graph structure
inherent in argumentation,
complete with inherent "multiple parents" and even cycles, but in
trying to clarity
and ease-of-use we have opted initially for simpler tree structures
and certain
generalizations (as seen in analysis mode).

We will be trying to relax this limitation somewhat in the not-too-
distant-future; the challenge is to
retain simplicity for everyone while not cramping the style of power-
users.

I can only imagine how difficult it must be to allow nodes to have
multiple parents. However, to the extent that _Rationale_ is used to
assess and construct evidential argument for forensic purposes, it is
important, in the long run, that _Rationale_ facilitate analysis of
problems of evidence and inference in which there are multiple parents
(i.e., generation-skipping and lateral links). Problems of evidence
and inference are shot through with argument structures that, in the
language of probability theory, involve dependent conditional
probabilities; and it is right to think of evidential inference, in
legal contexts, as ordinarily taking the form of a web rather than a
ladder or a tree. It is not an accident that much of the
"probabilities debate" in legal scholarship in the law of evidence has
centered on situations involving dependent conditional probabilities
(such as in the famous _Collins_ case and more recently in the
Maryland _Wilson_ case concerning sudden infant death syndrome and and
the extent to which [and the circumstances under which] multiple
possible SIDS deaths are evidence of criminal homicide or similar
crimes). I think the phenomenon of web-like inference is not peculiar
to legal contexts; I think it is more the rule than the exception. So
the ultimate real-world success and acceptability of _Rationale_ in
many domains may depend on Rationale's ability to, not just
accommodate, but facilitate the formation and assessment of web-like
inferential argument. True, this step makes the software development
task much more difficult [I imagine]. But this additional complexity
is a feature that the requirements of real-world inferential work
impose.

Your humble servant,

  Peter T

On Jun 17, 5:50 pm, Daniel Prager <daniel.a.pra...@gmail.com> wrote:

While a full graph- or web- structure is no doubt essential in certain
domains,
I do not think that it is necessary for this argument!

I invite you to construct a Rationale argument-map supporting the
less qualified contention:

     "The real-world success of _Rationale_ depends on Rationale's
      ability to facilitate the formation and assessment of web-like
      inferential argument."

Send it to dan-at-no-spam-austhink-dot-com and I will polish it up and
post it
on my blog.

-- Dan

On Jul 19, 10:21 pm, PeterT <peter.till...@gmail.com> wrote:

My thesis about the importance (prevalence) of web-like structures is
limited to evidential argument, or factual inference. (It is possible
that web-like arguments are important in other contexts as well. But
I'm not in  a position to make a judgment about that.) My best account
(though not necessarily the best account) of the importance of
evidential webs is in an essay that reviews David Schum's work. See
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=880130

Your even more humble servant,

   Peter T

P.S. I look forward to carrying on this discussion in person when I
visit Australia next March and April.

On Jul 19, 5:59 pm, Daniel Prager <daniel.a.pra...@gmail.com> wrote: