Abstract goes here
This study examines the problem of belief revision, defined
as deciding which of several initially-accepted sentences to disbelieve,
when new information presents a logical inconsistency with the initial
set. In the first three experiments, the initial sentence set included
a conditional sentence, a non-conditional (ground) sentence, and an inferred
conclusion drawn from the first two. The new information contradicted the
inferred conclusion. Results indicated that conditional sentences were
more readily abandoned than ground sentences, even when either choice would
lead to a consistent belief state, and that this preference was more pronounced
when problems used natural language cover stories rather than symbols.
The pattern of belief revision choices differed depending on whether the
contradicted conclusion from the initial belief set had been a modus ponens
or modus tollens inference. Two additional experiments examined alternative
model-theoretic definitions of minimal change to a belief state, using
problems that contained multiple models of the initial belief state and
of the new information that provided the contradiction. The results indicated
that people did not follow any of four formal definitions of minimal change
on these problems. The new information and the contradiction it offered
was not, for example, used to select a particular model of the initial
belief state as a way of reconciling the contradiction. The preferred revision
was to retain only those initial sentences that had the same, unambiguous
truth value within and across both the initial and new information sets.
The study and results are presented in the context of certain logic-based
formalizations of belief revision, syntactic and model-theoretic representations
of belief states, and performance models of human deduction. Principles
by which some types of sentences might be more "entrenched" than others
in the face of contradiction are also discussed from the perspective of
induction and theory revision.
This is a position paper concerning the role of empirical
studies of human default reasoning in the formalization of AI theories
of default reasoning. We note that AI motivates its theoretical enterprise
by reference to human skill at default reasoning, but that the actual research
does not make any use of this sort of information and instead relies on
intuitions of individual investigators. We discuss two reasons theorists
might not consider human performance relevant to formalizing default reasoning:
(a) that intuitions are sufficient to describe a model, and (b) that human
performance in this arena is irrelevant to a competence model of the phenomenon.
We provide arguments against both these reasons. We then bring forward
three further considerations against the use of intuitions in this arena:
(a) it leads to an unawareness of predicate ambiguity, (b) it presumes
an understanding of ordinary language statements of typicality, and (c)
it is similar to discredited views in other fields. We advocate empirical
investigation of the range of human phenomena that intuitively embody default
reasoning. Gathering such information would provide data with which to
generate formal default theories and against which to test the claims of
proposed theories. Our position is that such data are the very phenomena
that default theories are supposed to explain.
Simple belief-revision tasks were defined by a giving
subjects a conditional premise, (p-->q), a non-conditional premise, (p,
for a modus-ponens belief-set, or ~q, for a modus tollens belief-set),
and the associated inference (q or ~p, respectively). "New" information
contradicted the initial inference (~q or p, respectively). Subjects indicated
their degree of belief in the conditional premise and the categorical premise,
given the contradiction. Results indicated that the choice was a function
of the knowledge type expressed in the conditional form; when that knowledge
type was causal, the choice was affected by the number of disabling factors
associated with the causal relationship. A "possible worlds" interpretation
of the data is related to formal notions such as epistemic entrenchment,
used in normative models of belief revision, and to reasoning from uncertain
premises, from the human deduction literature.
Some belief revision theories appeal to the notion of
epistemic entrenchment as a guide to choosing among alternative ways of
removing inconsistency that new information may cause with existing beliefs.
While belief revision theorists may not be interested in natural language
uses of conditionals per se, the appeal to epistemic entrenchment because
certain kinds of knowledge (e.g., physical laws) are expressed in conditional
form opens the door to a more careful consideration of whether the syntactic
form itself serves as a useful cue, even in the mind of the researcher,
for epistemic entrenchment principles. This study determines whether there
is any empirical support for the notion that the type of knowledge expressed
in a statement can serve as the basis for epistemic entrenchment principles.
Four types of knowledge-- promises, causal relationships, familiar definitions
and unfamiliar definitions--were expressed in a common syntactic if p then
q form. A belief revision task was given to people, in which these conditionals
were used to define "initial belief" sentences, which were then followed
by a "new information" sentence that created an inconsistency with the
initial set of beliefs. The frequency with which people chose to disbelieve
the conditional (or lower their degree of belief in it) as a way of resolving
the inconsistency depended on the type of knowledge--causal, definitional,
or promises--that the conditional expressed. The conditionals that expressed
causal information were further analyzed according to the possible alternative
causes and disabling factors associated with the causal relationship. These
more subtle distinctions also affected how people revised the belief sets
using causal scenarios. For normative belief revision models, such findings
call into question the notion that conditionals ought to be more entrenched
by virtue of their syntactic form. They also question whether the syntactic
if-then form of conditionals can even serve as a useful cue for signaling
the types of knowledge that it might be plausible to entrench, such as
causal relationships. These results support higher-order epistemic entrenchment
principles that distinguish among types of knowledge (regardless of the
syntactic form in which they are expressed) and known necessity and sufficiency
aspects of causality relationships in particular.
We report empirical results on factors that influence how people reason with default rules of the form "Most x's have property P", in scenarios that specify information about exceptions to these rules and in scenarios that specify default-rule inheritance. These factors include (a) whether the individual, to which the default rule might apply, is similar to a known exception, when that similarity may explain why the exception did not follow the default, and (b) whether the problem involves classes of naturally occurring kinds or classes of artifacts. We consider how these findings might be integrated into formal approaches to default reasoning and also consider the relation of this sort of qualitative default reasoning to statistical reasoning.
We report empirical results on factors that influence human default reasoning, both in feature-inheritance type problems and in problems that specify information about exceptions to default rules. These factors include similarity between instances that are reasoned about and whether the classes of the instances are naturally- occurring or classes of artifacts. While in classical deductive logic, a problem's 'correct answer' is defined by the problem's formal structure, we argue that the case is different for default reasoning. The identification of factors that influence people's default inferences can contribute to more robust theories of default reasoning that include principles of relevance.
In this paper we report preliminary results on how people revise or update a previously held set of beliefs. When intelligent agents learn new things which conflict with their current belief set, they must revise their belief set. When the new information does not conflict, they merely must update their belief set. Various AI theories have been proposed to achieve these processes. There are two general dimensions along which these theories differ: whether they are syntactic-based or model-based, and what constitutes a minimal change of beliefs. This study investigates how people update and revise semantically equivalent but syntactically distinct belief sets, both in symbolic-logic problems and in quasi-real-world problems. Results indicate that syntactic form affects belief revision choices. In addition, for the symbolic problems, subjects update and revise semantically-equivalent belief sets identically, whereas for the quasi-real-world problems they both update and revise differently. Further, contrary to earlier studies, subjects are sometimes reluctant to accept that a sentence changes from false to true, but they are willing to accept that it would change from true to false.