Logic, the science of argument or reasoning, has since the days of Aristotle very largely focused on exact reasoning, i.e. reasoning with statements which are either true or false (but not both). Over the intervening two and a half millenia this has produced some very nice mathematics, yet very little of it can be said to be directly relevant to the way we reason in our everyday lives. Most of our reasoning involves using knowledge which we would readily admit to being to some extent uncertain to start with. For example whenever we plan a trip we need to build in numerous uncertain features about the credibility of time tables, weather conditions, traffic congestion etc.
Over the past twenty years however the situation has changed dramatically, and considerable research effort and funding has gone into trying to understand uncertain knowledge, how to represent it, and how to reason with it intelligently. The cause of this sudden interest has been the rising power of computers and the dream of having `intelligent' computers, computers which can, like us, draw useful conclusions even when their knowledge is less than precise.
Despite so much interest the central questions remain largely unanswered. What is `knowledge'? What does it mean to act `intelligently'? Given the apparently very modest power of our own brains to perform computations, how is it possible for us to be as smart as (we think) we are? These are challenging questions in a fundamental area and they cry out for new ideas and theories, all the more so because progress to date has so abjectly failed to fulfill the early predictions. There is a feeling that there are cornerstone theorems here waiting to be discovered, theorems which could have a profound influence in IT and hence in all our lives.
Here at Manchester the Uncertain Reasoning Group are investigating these questions, in particular through the idea of identifying 'intelligence' with observance of common sense principles, in both propositional and predicate reasoning. Our approach is theoretical and logic based although it touches on a number of other domains, particularly probability theory, analysis and several areas of philosophy. Because of its perceived relevance it is a comparatively well funded research area and graduates' skills and knowledge generally ensure them ready employment in the IT industry.