Introduction to Non-Monotonic Logic

Mathieu Beirlaen and Christian Strasser

  • Area: LoCo
  • Level: I
  • Week: 2
  • Time: 11:00 – 12:30
  • Room: D1.03


Informally, a logic is non-monotonic if under the addition of new premises we may lose some consequences which were previously derivable. This means that some of our inferences are defeasible: in view of additional information they may get retracted. Examples of defeasible reasoning patterns are numerous: induction, inference to the best explanation, inferences on the basis of expert opinions, reasoning in the presence of inconsistencies, reasoning with priorities, etc. In our everyday practice as well as in the practice of experts (e.g. medical diagnosis) or scientists, defeasible inferences are abundant.

In this course, we present, discuss, and compare some of the principal formalisms for representing defeasible inferences via non-monotonic logics. We introduce the framework of inheritance networks, Reiter’s default logic, argumentation frameworks, preferential semantics, and adaptive logics. Each of these frameworks is representative of a large research tradition within the field of non-monotonic logic. In our course the interested student gets equipped with a basic understanding that will enable her to dig deeper into the literature and to understand similar techniques in formalisms that are not covered in the course.


Slides day 1 (preferred models)

Slides day 2 (adaptive logics)

Slides day 3 (maximal consistent subsets)

Slides day 4 (default logic)

Slides day 5, part 1 (abstract argumentation)

Slides day 5, part 2 (structured argumentation)

Additional References

Bibliography (days 1 and 2)