Speaker:

Willem Labuschagne, Department of Computer Science

Title:

Everything you ever wanted to know about nonmonotonic logic

Location:

Archway 2 - 1:00 pm, Friday 27 August

Abstract:

A child as young as 9 months is already capable of the kind of reasoning known as induction. Give the child a cylindrical can to play with, a can cunningly designed to have the non-obvious property that it makes a mooing sound when it is turned over. If subsequently given a new can with a different colour and pattern on the outside, the child will turn it over in an attempt to produce the sound. Controls who initially received a can that did not make a sound, do not attempt to produce the sound on the new can. Thus this study by Baldwin, Markman and Melartin shows that even young children form expectations based on category membership: new objects about which not much is known are expected to share the features of typical members of their category.

Nonmonotonic logic was invented in the 1980s in order to formalise this kind of reasoning, known variously as categorical induction, individual case induction, or singular predictive inference.

I present one particular approach to nonmonotonic logic, an approach that over the past two decades has become the main line, and ask five fundamental questions:

• How does nonmonotonic logic differ from classical logic?
• Can classical logic be used to explain categorical induction?
• How does nonmonotonic logic differ from the use of probabilities?
• Can nonmonotonic logic be reduced to a form of probabilistic reasoning?
• What is the relationship between nonmonotonic logic and the equally new approach called AGM belief change theory?