Statement of Plans by Neil Tennant

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					Belief-Revision                                                               Page 1 of 3
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Description of the problem. John has called his engagement off. For he has just discovered that Mary has a
dark secret. The discovery conflicts with many of his previously cherished beliefs about her. He no longer
believes she is trustworthy. Nor does he believe that they will marry. But should he change any of his beliefs
about the institution of marriage?—or about the battle between the sexes? How far should his belief-
revisions go? Second example: Bertrand has pointed out a contradiction in the foundations of Gottlob’s
logical system for mathematics. Gottlob has to give something up, in order to restore consistency. But what
claims should he retract? And what will be the impact on Gottlob’s commitment to the higher reaches of the
edifice that he had built on those foundations?
         Rational revision of beliefs, in our personal affairs and in our intellectual lives, is critical. The task
can be simply stated, for an ideally rational agent, as follows. Suppose the agent’s current system of belief
implies a particular proposition, which the agent now realizes is false. Thus the agent wishes to believe the
negation of that proposition, and to mutilate the system as little as possible in coming to do so. First, the
agent must contract the system—give the proposition up, along with anything in the system that either
implies, or wholly depends on it. Then the agent will add the desired negation to the contracted result.
         We need a rigorous account of this operation of contraction. How wide-ranging ought it to be? What
constrains a rational mind from throwing the baby out with the bathwater? Philosophers of science talk of
‘minimally mutilating changes in the web of belief’, but specify no precise way to effect them. Hence the
current project: give a philosophically sound, mathematically precise account of contraction, programmable
on a computer. The account will be normative, not descriptive. Why? Because we need to know what ought
to be done by an ideally rational agent confronted with the need to change its mind. I want to offer an
instrument of refined rationality, with tremendous scope and power. Successful automation of the task of
belief-revision would bring widespread applications. These range from specialized fields such as medical
diagnostics, to more general predictive and explanatory frameworks in the natural sciences. Wherever beliefs
are organized with articulated reasons, the proposed methods of rational revision would apply.
         A new account of theory-contraction and revision will have to be interdisciplinary. First there are
important epistemological issues to be resolved. These concern whether belief systems are finite (can our
finite minds entertain only finitely many beliefs?); epistemic priority (what counts as a reason for what?);
and possible patterns of justificatory regress (can justifications form loops? can they backtrack forever, or
must they terminate?). Secondly, the systematic character of the essential components and structures
involved in rational belief-systems motivates a more precise logical theory. This logical theory provides the
mathematical means to represent belief-systems, as well as the computational means to manipulate and
transform them. Moreover, the theory, though logical, turns a blind eye to the logical structure within the
agent’s beliefs; it attends only to the justificatory relations, for the agent, among them.
         The technical part of the theory will present mathematical details of so-called ‘finite dependency
networks’ from first principles. Such networks model patterns of justificatory relations. They enable one to
explicate the notion of minimal mutilation and precisely define the problem of contraction. One can then ask
how complex the contraction problem is—that is, how much time and memory space are needed for the
computation, depending on the size of input. It turns out to be exactly as complex as the problem of deciding
whether one can make a given formula of sentential logic true by assigning appropriate truth-values to its
sentence-letters. (The technical term is ‘NP-complete’.) I shall specify efficient contraction algorithms, and
implement them in Prolog (the high-level language for programming in logic). Then I shall illustrate the
new methods by applying them to the various problems that have appeared in the literature by way of
criticism of extant theories of contraction and revision. I shall show that the new account handles these
problems in a way that would appeal to any intelligent person uncorrupted by implausible theories of
revision. The contraction algorithms will also deal with relative entrenchment among beliefs, which is
important for epistemologists concerned with real-world modelling of belief-systems.

Philosophical Significance. The form of representation of belief-systems that this account employs for
computational purposes helps to illuminate the commonalities and differences among the major positions
held by epistemologists. These positions are the best-known responses to the problem of ‘regress of

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Outline for Research Seminar PHIL 860
Belief-Revision                                                               Page 2 of 3
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justification’. Foundationalists think chains of justification must terminate, whereas coherentists will tolerate
‘loops’. Now, logicians have sought to provide a unified framework in proof theory allowing for variant
systems of deductive reasoning (such as classical, constructive or relevance logic) with rules of inference
tailored to various presuppositions about truth and meaning. These deductive systems enable the reasoner to
move rigorously and efficiently within a theory. For belief-revision, then, we should likewise seek to provide
a unified framework in the theory of theory-change allowing for variant epistemological positions (such as
foundationalism, coherentism or foundherentism) with contraction methods tailored to various
presuppositions about rational belief and justificatory structure. Such systems would enable the reasoner to
move rigorously and efficiently from theory to theory.
         The new account of rational belief-revision can also help identify the inviolable core of logic—those
forms of inference essential to the task of revision itself, and hence immune to revision in the light of any
experiences, no matter how unexpected they may be. It could also be extended to handle retractions of
justificatory steps themselves, in addition to the beliefs serving as their premises and conclusions.
         The behavior of the new contraction algorithm deserves to be investigated systematically on many
larger problem-sets, in search of regularities involving the initial structure of a belief-system and the variety
of ways in which one can contract it. Of particular interest will be phase-transition or threshold phenomena
such as those encountered at times of theoretical crisis, when many anomalies have cropped up. Thomas
Kuhn talks of ‘paradigm shifts’, or revolutionary theory-change—such as the shift from Newtonian
dynamics to Einsteinian relativity theory. What prepares the ground for such a shift? Why does the old
theory suddenly implode under the force of the contractions demanded by experience? How does contraction
in response to bits of evidence induce large-scale theoretical collapse? Might there be a more deeply rational
process at work than some of Kuhn’s followers have claimed? I seek to throw new light on these questions.

Computational Significance. On my analysis, the contraction problem is of the lowest level of complexity
that one can hope for with a non-trivial logic problem. This is a strong point in favor of the new account.
The resulting computational theory affords the most efficient tests possible of implementations of one’s
contraction algorithms on a wide range of inputs. Such tests can yield theoretical insights as to how
variously structured belief-systems undergo contractions with respect to variously positioned consequences.

Relation to present state of the field. The sought account will differ from the logicians’ prevailing theory
of theory-change, called AGM-theory. It will also differ from the AI-community’s theory of Justification-
based Truth-Maintenance Systems. This is for the following reasons, which are perforce very brief. First, no
one can implement AGM-theory on a computer, for it does not treat belief-systems as finite. Moreover, its
main so-called Postulate of Recovery (about what happens if one retracts a belief and then re-adopts it)
succumbs to striking counterexamples. Also, its methods of contraction (involving complicated set-theoretic
operations) mutilate theories too much. Secondly, JTMS-theory handles logical truths incorrectly (as
supposedly potent premises), and non-foundationalist epistemologies not at all. It retracts only assumptions,
and fails to deal with the general operation of contracting a belief-system with respect to arbitrary unwanted
consequences.
         The sought account should remedy these shortcomings, and achieve further important goals. It
should justify the claim that representing belief-systems as finite dependency-networks (as a computational
account must do) incurs no loss of generality, and no restriction in the scope of applicability. It should
explicate the notion of minimal mutilation, and establish how complex the contraction problem is. By
working on the way we employ justificatory relations among propositions when contracting a belief-system,
I aim to uncover the essential features of theory-change in general, without resorting to non-standard
revisions of the underlying logic itself.

NT
May 2003


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Outline for Research Seminar PHIL 860

				
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