Modelling Experiments - Natural and Artificial Reasoning - page 65

The cycle 'abduction (generation) deduction (prediction) induction (validation)
the inference abduction' reflects something of the scientific process of interpreting
new or surprising findings by generating a hypothesis whose consequences are then
evaluated empirically (Hanson 1958 ; Gooding 1996 ). However, an abduction cycle
calls for sensitivity to empirical context. This in turn calls for variability in the set of
descriptors and for some plasticity in their meaning (for examples see Gooding 1990 ).
This plasticity of meaning requires a kind of set for which there is no finite collection
of rules that establish membership of an element; we must be able to change mem-
bership by adjusting the set of rules that can be applied. Such sets mediate between
the stable language of formal models and the changing, often uncertain contexts to
which they apply. Scientists work out the rules governing set-membership as they
develop the experimental and theoretical methods of a domain.

We will call such dynamic and flexible sets irrational .

We will illustrate this through a computational model of beliefs represented as the
level of confidence in each of a set of hypotheses. These beliefs can be revised in the
light of new information (Addis and Gooding 1999 ; Gooding and Addis 1999 , 2004 ).
This model will show how abduction, as part of a larger inference system, can make
the world a less surprising place. In order to implement it as an iterative model, we
must first articulate the notion of abduction in terms of a measure of expectation.

The most appropriate measure of expectation 1 is called entropy 2 .

However, we found that when we try to minimize this measure through an agent's
actions so as to make the world a less surprising place then this measure produced
implausible behaviour. In particular, simulated agents will become locked into fixed
patterns of belief and behaviour.
The entropy measure works only if it is:

i. continually validated and adjusted
ii. incorporates random actions based upon game theory.

Our simulation experiments suggest, therefore, that rules governing membership in
irrational sets require:

i. a continuous reappraisal and revision
ii. the possibility of actions that appear irrational.
The set of beliefs is irrational in that its membership can change (e.g., to include new
descriptors for surprising or anomalous information, Gooding 1990 ), even without
recourse to definitions or correspondence rules (Kuhn 1974 , pp. 310-312). Behaviour

1 Also referred to as surprise
2 As described by Shannon and Weaver, 1964