Embedding abduction in nonmonotonic theories

Abstract

An important ampliative inference schema that is commonly used is abduction. Abduction plays a central role in many applications, such as diagnosis, expert systems, and causal reasoning. In a very broad sense we can state that abduction is the inference process that goes from observations to explanations within a more general context or theoretical framework. That is to say, abductive inference looks for sentences (named explanations), which, added to the theory, enable deductions for the observations. Most of the times there are several such explanations for a given observation. For this reason, in a narrower sense, abduction is regarded as an inference to the best explanation. However, a problem that faces abduction is the explanation of anomalous observations, i. e., observations that are contradictory with the current theory. It is perhaps impossible to do such inferences in monotonic theories. For this reason, in this work we will consider the problem of characterizing abduction in nonmonotonic theories. Our inference system is based on a natural deduction presentation of the implicational segment of a relevant logic, much similar to the R! system of Anderson and Belnap. Then we will discuss some issues arising the pragmatic acceptance of abductive inferences in nonmonotonic theories.