Explanatory relationships can be used effectively to reduce the uncertainty that remains after diagnostic hypotheses have been scored using local matching

Josephson, John R.

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N89-19831 
Reducinq Uncertainty by Using Explanatory Relationships 
John R. Josephson, Ph.D., The Ohio State University 
Abstract 
Explanatory relationships can be used effectively to reduce the 
uncertainty that remains after diagnostic hypotheses have been 
scored using local matching. 
1. Introduction 
The problem that the mind must solve is not that of reasoning 
with uncertainty, but reasoning DESPITE uncertainty -- how to 
come to robust conclusions despite uncertain data, inconclusive 
inference procedures, and incomplete knowledge. 
(-- B. Chandrasekaran) 
Suppose that some black box hypothesis source delivers up a 
set of diagnostic hypotheses, each hypothesis given a confidence 
value on some scale. Suppose further that these confidence 
values can be taken to reflect “local match” or prima facie 
likelihood. That is, the confidence value associated with each 
hypothesis is a measure of its likelihood of being true, based only 
on consideration of the match between the hypothesis and the 
data with little or no consideration of interactions between 
potentially rival or otherwise related hypotheses. Thus we have a 
picture of a set of hypotheses where each has been somehow 
stimulated, evoked, and instantiated for the case, and at the 
current stage of processing each hypothesis has been scored ir 
isolation from the others. 
At this stage we have both a problem, and an opportunity to do 
something about it. The problem is that many hypotheses will 
probably have intermediate scores, representing hypotheses that 
can neither be taken as practically certain. nor as being of such a 
low confidence as to be ignorable. Some number of these 
hypotheses are presumably true, but how many and which ones? 
The opportunity is that of bringing knowledge of interactions 
between the hypotheses to bear in order to reduce the degree of 
uncertainty associated with the hypotheses -- increasing 
confidence in some of them, and decreasing conlidence in others. 
Some types of interactions between hypotheses are: 
A and B are mutually incompatible. 
A is a more detailed refinement of B. 
A could be caused by 8. 
A and B are mutually compatible, and are explanatory 
alternatives where their explanatory coverages 
overlap. 
Besides hypothesis--hypothesis interactions of mutual 
incompatibility and support, which can arise by degrees as well as 
discretely, one especially interesting class of interactions concerns 
explanatory relations: what happens when two or more 
hypotheses represent alternative explanations for the same 
datum? The focus of this paper will be on explanatory 
relationships, and on how explanatory relationships impact on our 
estimates of confidence. 
Knowledge of explanatory relationships gives us an opportunity 
to take advantage of some “best explanation” reasoning. 
2. Best-Explanation Reasoning 
inference that follows a pattern approximately like this:’’ *, 3, 
lnference to the Best Explanation or Abduction is a form of 
D is a collection of data (facts, observations, 
givens), 
H explains D (would, i f  true, explain D), 
No other hypothesis explains D as well as H does. 
Therefore. H is correct. 
...__.______________~~~-.~--~~~~~~~~~~--~~-~~....-.----- 
The strength of an abductive conclusion will in general depend 
on several factors, including: 
the alternatives, 
how good H is by itself, independently of considering 
how decisively H surpasses the alternatives, 
how thorough the search was for alternative 
pragmatic considerations, including 
explanations, and 
*the costs of being wrong and the benefits of 
being right, 
* how strong the need is to come tu a conclusion 
at all. especially considering the possibility of 
seeking further evidence before deciding. 
149 
https://ntrs.nasa.gov/search.jsp?R=19890010466 2020-03-20T04:08:42+00:00Z
Abductions, as we have just characterized them, go from data 
&scribing something to an explanatory hypothesis that best 
accounts for that data. 
3. Using Explanatory Relationships 
Let us suppose that, besides a confidence value, each plausible 
diagnostic hypothesis (one which is not ruled-out) is associated 
with a description of which findings that hypothesis can explain. 
One way to take advantage of these explanatory relationships is 
to set up a standard for when a diagnosis is complete. The 
diagnosis can be considered to be complete when all of the 
abnormal findings have been accounted for (explained). (This 
standard should be considered to be somewhat of an idealization, 
since for example unimportant findings need not be accounted 
for.) 
Let us focus on the use of explanatory relationships to reduce 
the uncertainty that remains after the confidence scoring based on 
local matching. First we note that an overall abduction problem is 
set up - to account for all of the (abnormal) findings, and a series 
of small abduction problems is set up - to account for each 
particular (abnormal) finding. Our basic strategy will be to try to 
solve the overall abduction problem by solving some number of 
smaller and easier abduction problems. 
First we solve the easiest little abduction problems, the ones in 
which we can have the most confidence. If a certain hypothesis is 
the only plausible explanation for some finding, then (supposing its 
local-match confidence value is not too low) it is entitled to as high 
confidence value, and entitled to be accepted into the overall 
composite hypothesis that represents the solution to the overall 
abductive problem. So first we form the set ofEssential 
hypotheses consisting of those of the sort we have just mentioned. 
If we are lucky the set of Essential hypotheses will together 
account for all of the (important abnormal) findings. If this occurs 
then the overall abduction problem is solved - the set of Essentials 
together constitutes the best explanation - and the diagnosis is 
complete. Hypotheses which are not part of this best explanation 
are lowered in confidence, since they are not needed as part 01 
the final explanation, and everything that they explain can now bc 
explained in some other (and in the context better) way. 
If the Essentials do not explain everything, then next we form 
the set of Clear Best hypotheses consisting of those which 
explain findings for which there is no other explanation anywhere 
nePr as good. For example if some finding S can only be 
ex1 lained by A (moderate confidence), B (low confidence), and C 
(lotv confidence), then A is worthy of acceptance as being clearly 
the best way to explain S. Hopefully, the Essentials together with 
the Clear Bests will now explain everything, and the diagnosis can 
be considered to be complete (after perhaps removing some few 
hypotheses which are now explanatorily superfluous in the 
presence of the rest). 
If the Essentials together with the Clear Bests do not explain 
everything we have done all we can do on the current evidenr 
without resorting to guessing Generally our best strategy undnr 
thc se circumstances would be to gather more data In 1 x 1  we ,ire 
in a position to guide our data gathering by focusing on the 
problem of discriminating between alternative good explanations 
for important findings. 
Yet sometime we have to decide quickly, and do not have 
enough time to gather further data. Also sometimes the cost of 
gathering further data is too high. Under these circumstances we 
still have the means available to do some clever guessing We can 
begin to include hypotheses which are best explanations for 
certain finding, but which are not far enough ahead of the 
alternatives, or not of high enough local-match confidence, to 
enable them to be accepted confidently. These Weakly Bests 
constitute the best guesses we can make under the 
circumstances. 
Actually we can even do slightly better. Findings can be made 
to vote for the hypotheses which best explain them. The idea is 
that two different findings both pointing to the same hypotheses as 
the best explanation constitute (apparently) independent sources 
of evidence for the hypothesis, Le. constitute converging lines of 
inference for the hypothesis. Hypotheses with more votes can be 
accepted more confidently than hypotheses with fewer votes, and 
enough can be accepted to complete the explanation. This 
phenomenon of converging lines of inference seems to be what 
the philosopher of science William Whewell (1794-1 866) called 
“the concilience of inductions.” 
4. Conclusion 
We have shown how a stage of diagnostic problem solving, 
where there are N viable plausible hypotheses, each with a 
confidence score based on local matching, can, by using 
explanatory relationships, be brought to a more advanced stage, 
where the number of hypotheses has been radically pruned to k 
hypo heses together representing a single compound hypothesis 
that f xDlains a distinct oortinn of the data. and which is a “lorjica Iv 
optimal” outcome in an abductive sense. I should point out that 
variations of this method have played an important role in several 
knowledge-based systems including the Red system for Red-cell 
antibody identification5 and the Pathex system for diagnosing 
cholestatic liver diseases. 
Note that, at the level of description we have been using, we 
might be describing the information processing of an “algorithmic 
computer”, i.e. an instruction follower; or a “connectionist 
cmputer”, i.e. one whose primitive processing elements work by 
propagating nudges and activation strengths. In either case what 
we are describing is the functional and semantic significance of 
various actions of the machine, not precisely how these actions 
are accomplished. 
Note too that we might be describing a medical diagnosis 
engine, or a diagnoser of mechanical systems, a fragment of the 
processing of the vertebrate visual system, or the information 
processing that goes on when we recognize words in continuous 
speech. The strategy for reducing uncertainty that we have 
described is appropriate quite generally for a variety of abductive 
or interpretive infor nmon processing tasks. 
150 
5. Acknowledgments 
Michael C. Tanner and Ashok Goel of Ohio State have 
contributed significantly to the development of these ideas, which 
have also benefited greatly from discussions with Jack Smith, Jr. 
and William Punch. This research has been supported in part by 
the Defense Advanced Research Projects Agency, RADC 
Contract F30602-85-C-0010 under the Strategic Computing 
Program, in part by the National Library of Medicine under grant 
LM-04298, and in part by the National Heart Lung and Blood 
Institute under grant HL-38776. Computer facilities have been 
enl- mced through gifts from Xerox Corporation. 
References 
1. 
2. 
3. 
4. 
5. 
Josephson, John R., “A Mechanism for Forming 
Compositer Explanatory Hypotheses”, /€E€ Transactions 
on Systems, Man and Cybernetics, Special lssue on 
Causal and Strategic Aspecfs of Diagnostic 
Reasoning,Vol. SMC-17, No. 3, May, June 1987, pp. 
445-54. 
Peirce, C.S., Abduction and Induction, Dover, 1955, pp. 
150lf., ch. 11. 
Pople, H., “On the Mechanization of Abductive Logic”, 
Proceedings of the Third lnternational Joint Conference on 
Artificial Intelligence, 1973, pp. 147-1 52. 
Eugene Charniak and Drew McDermott, lntroduction to 
Artificial Intelligence, Addison Wesley, 1985. 
Smith, Jack W.; Svirbely, John R.; Evans, Charles A.; 
Strohm, Pat; Josephson, John R.; Tanner, Mike, “RED: A 
Red-Cell Antibody Identification Expert Module”, Journal of 
MedicalSystems,Vol. 9, No. 3, 1985, pp. 121-138. 
151 


Reducing uncertainty by using explanatory relationships

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