The Idea of Defeasibility
In a very broad sense, the idea of defeasibility may be applied to any
process that responds to its normal inputs with certain outcomes (the
default results), but which delivers different outcomes when such inputs
are augmented with further, exceptional or abnormal elements.
The computer scientist and theorist of complexity John Holland argues
that complex systems—such as a cell, an animal, or an ecosystem—can
be characterised “in terms of a set of signal-processing rules called
classifier rules” (Holland 2012, 28). Each such rule represents a
mechanism which “accepts certain signals as inputs (specified by the
condition part of the rule) and then processes the signals to produce
outgoing signals (the action part of the rule).” He observes that
complex systems need to address different situations, requiring
different responses, which are triggered by rules having different
levels of generality. In many cases the most efficient way to cover
multiple different contingencies consists in constructing “a hierarchy
of rules, called a default hierarchy, in which general rules cover the
most common situations and more specific rules cover exceptions”
(Holland et al 1989). Thus, a general rule would provide the normal
response to a certain input, but more specific rules would override the
general rule in exceptional situations, in which a different response is
needed. The emergence of default hierarchies may be favoured by
evolution, since such hierarchies may contribute to the fitness of the
systems using them.
Default hierarchies offer several advantages to systems that learn or
adapt:
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A default hierarchy has many fewer rules than a set of rules in which
each rule is designed to respond to a fully specified situation.
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A higher-level rule […] is easier to discover (because
there are fewer alternatives) and it is typically tested more often
(because the rule’s condition is more frequently satisfied.
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The hierarchy can be developed level by level as experience
accumulates (Holland 2012, 122).
This perspective can be applied to different domains at different levels
of abstraction. For instance, at the cellular level rule mechanisms
specify the catalytic and anti-catalytic processes that induce and
inhibit chemical reactions. At the DNA level, rule mechanisms are
provided by genes (and parts of them): a gene delivers the protein
matching the sequence of the gene’s bases. A gene may be regulated by
other genes that send signals that under particular conditions repress
(turn off) or induce (turn on) the functioning of the gene rule at
issue. Animal behaviour is also largely governed by systems of reflex
rules defining reactions to heat or cold; or to the sight, smell, or
taste of food; or to the perception of incoming dangers; and so on. Such
reflexes can be innate or learned by experience, i.e., by conditioning
and reinforcement. They may interact in complex patterns where some
reflexes are stronger than others, so that they determine the response
in cases of conflict, or they may have an inhibitory impact on other
reflexes, blocking them under particular situations. In humans, reflexes
are integrated with deliberative processes and means-end reasoning, but
still they govern a large part of human behaviour.
As Holland et al. (1989, 38) argue, not only instinctive reflexes but
also mental models can be based on sets of prioritised default rules:
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The rules that constitute a category do not provide a definition of
the category. Instead they provide a set of expectations that are
taken to be true only so long as they are not contradicted by more
specific information. In the absence of additional information these
“default” expectations provide the best available sketch of the
current situation. Rules and rule clusters can be organized into
default hierarchies, that is, hierarchies ordered by default
expectations based on subordinate/superordinate relations among
concepts. For example, knowing that something is an animal produces
certain default expectations about it, but these can be overridden by
more specific expectations produced by evidence that the animal is a
bird.
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In conclusion, a defeasible process can be as characterized a mechanism
which responds to its normal inputs with certain default outcomes, but
that may fails to respond in this way, when the input is accompanied by
certain additional exceptional elements.