We argue that abduction does not work in isolation from other inference mechanisms and illustrate this through an inference scheme designed to evaluate multiple hypotheses. We use game theory to relate the abductive system to actions that produce new information. To enable evaluation of the implications of this approach we have implemented the procedures used to calculate the impact of new information in a computer model. Experiments with this model display a number of features of collective belief-revision leading to consensus-formation, (...) such as the influence of bias and prejudice. The scheme of inferential calculations invokes a Peircian concept of ‘belief’ as the propensity to choose a particular course of action. (shrink)

We argue from the Church-Turing thesis (Kleene Mathematical logic. New York: Wiley 1967) that a program can be considered as equivalent to a formal language similar to predicate calculus where predicates can be taken as functions. We can relate such a calculus to Wittgenstein’s first major work, the Tractatus, and use the Tractatus and its theses as a model of the formal classical definition of a computer program. However, Wittgenstein found flaws in his initial great work and he explored these (...) flaws in a new thesis described in his second great work; the Philosophical Investigations. The question we address is “can computer science make the same leap?” We are proposing, because of the flaws identified by Wittgenstein, that computers will never have the possibility of natural communication with people unless they become active participants of human society. The essential difference between formal models used in computing and human communication is that formal models are based upon rational sets whereas people are not so restricted. We introduce irrational sets as a concept that requires the use of an abductive inference system. However, formal models are still considered central to our means of using hypotheses through deduction to make predictions about the world. These formal models are required to continually be updated in response to peoples’ changes in their way of seeing the world. We propose that one mechanism used to keep track of these changes is the Peircian abductive loop. (shrink)

In this paper we describe in some detail a formal computer model of inferential discourse based on a belief system. The key issue is that a logical model in a computer, based on rational sets, can usefully model a human situation based on irrational sets. The background of this work is explained elsewhere, as is the issue of rational and irrational sets (Billinge and Addis, in: Magnani and Dossena (eds.), Computing, philosophy and cognition, 2004; Stepney et al., Journey: Non-classical philosophy—socially (...) sensitive computing in journeys non-classical computation: A grand challenge for computing research, 2004). The model is based on the Belief System (Addis and Gooding, Proceedings of the AISB’99 Symposium on Scientific Creativity, 1999) and it provides a mechanism for choosing queries based on a range of belief. We explain how it provides a way to update the belief based on query results, thus modelling others’ experience by inference. We also demonstrate that for the same internal experience, different models can be built for different actors. (shrink)