Interpolation of benchmark problems in defeasible reasoning
Gerard A. W. Vreeswijk · 1995
Defeasible reasoning is the kind of logic in which further inference may cause a retraction of former conclusions. Recently, the research program of defeasible reasoning seems to be driven by a set of simple case studies, called benchmark problems, that are used to indicate the strength (or weakness) of particular modes of defeat. In doing so, the aim is to solve as much benchmark problems as possible. With reference to this somewhat pragmatic research method, the present paper reports on research on a very interesting and much overlooked question: just how much does it mean when a logician claims that his system of defeasible reasoning ‘captures many of the important benchmark problems’? To answer that question, we formulate an interpolation theorem for defeasible reasoning. This interpolation theorem will be formulated in precise terms, and will be proven formally. As a result, the positive statement that a formalism solves a particular set of benchmark problems looses much of its informative content. Research area 1985 Mathematics subject classification 68C01; 1987 CR classification scheme F.4.0, I.2.3, key words and phrases: defeasible reasoning, nonmonotonic logic.