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Grigoris Antoniou, D. Billington, and M.J. Mahler

Sceptical logic programming based default reasoning - Defeasible logic rehabilitated.

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Overview of interactions

N:o Question Answer(s) Continued discussion
1 9.1  Bob Kowalski
2.2  Grigoris Antoniou
2 9.1  Michael Thielscher
2.2  Grigoris Antoniou
9.1  Erik Sandewall
9.1  Michael Thielscher
9.1  Erik Sandewall
2.2  Grigoris Antoniou
3 9.1  Erik Sandewall
4 9.1  Alessandro Provetti
9.1  Grigoris Antoniou
5 9.1  Erik Sandewall
9.1  Grigoris Antoniou
9.1  Bob Kowalski
6 9.1  Graham White
9.1  Grigoris Antoniou
9.1  Pat Hayes
9.1  Graham White
9.1  Pat Hayes
9.1  John McCarthy
9.1  Pat Hayes
7 9.1  Bob Kowalski
2.2  Grigoris Antoniou

Q1. Bob Kowalski:

How is your representation related to Pollack's theory of argumentation?

A1. Grigoris Antoniou (2.2):

We have not yet compared DL to Pollock's work, but comparison to argumentation frameworks is next on our agenda.

Q2. Michael Thielscher:

The conclusions that your logic gives for example 4.5 (a modified Nixon diamond example) seem to indicate that your logic is plain wrong. The conclusions that you obtain are not in line with common sense.

A2. Grigoris Antoniou (2.2):

The statement that the outcome is "plain wrong" is questionable. This debate has already been held in the context of inheritance systems. Where "a clash of intuitions" exists nobody can claim that one particular approach is THE common sense approach.

What may cause some confusion in the present example is a feeling one might have that antimilitary and pacifist are the same. Not eveybody agrees on this (not even the authors among themselves!) but if it helps, replace "antimilitary" by another predicate semantically unrelated to all the others.

C2-1. Erik Sandewall:

In answer to Thielscher: but if unintended conclusions are obtained, then one ought to consider that the problem is with the axiomatisation and not with the logic itself.

C2-2. Michael Thielscher:

(To Sandewall) Do you think it is the fault of the axiomatization in this case?

C2-3. Erik Sandewall:

I would certainly hope so. More generally, since a variety of different strategies for multiple inheritance with exception has been studied in the specialized literature on that topic, one ought to require from a nonmonotonic logic that is used for this purpose that it be capable of expressing several of these inheritance strategies, and not just one of them.

C2-4. Grigoris Antoniou (2.2):

In a default logic setting sceptical reasoning is obtained by considering the intersection of extensions. One might say that defeasible logic takes a more intelligent approach by reasoning along the way what will and will not be part of this intersection, and makes use of this information accordingly.

Regarding the axiomatization of example 4.5, if one takes the view that antimilitary and pacifist are the same, then indeed they should be represented as one predicate. In that case we would get an undisputed result (nothing can be proven about pacifist/antimilitary).

Q3. Erik Sandewall:

In response to your question during the workshop presentation about references to similar or related work in the literature, I suggest that there is an apparent relation to hypothesis logics, which have been developed by several authors. The difference is as follows: in your logic, tagged formulae using the operator  \partial  appear in the conclusions, but not in the theories from which conclusions are obtained. In hypothesis logics, on the other hand, tagged formulae can be used everywhere, and therefore one does not need the additional types of implication that you use. Instead of formulae of the form  bird(x) typically-implies flies(x, hypothesis logics use formulae of the form  bird(x) implies default(flies(x)) . (Exact references will be added).

Q4. Alessandro Provetti:

(Question not recorded).

A4. Grigoris Antoniou:

We believe that our type of theory, which uses rules plus a priority relation, is strictly more expressive than rules plus negation as failure. (References).

Q5. Erik Sandewall:

I also have a question about your motivation for introducing a new nonmonotonic logic for the explicit purpose of commonsense reasoning. It seems to me that there is only a limited number of uses of nonmon reasoning, and that each of those application is being studied by separate methods and area-specific techniques. Multiple inheritance and reasoning about actions are two examples of such uses; there are of course a few more but not so many. Given this, wouldn't it be better to view nonmonotonic logics as instruments that are to be used for the area specific developments? Relating a nonmon logic directly to specific examples of commonsense reasoning seems to take in one step what would be better analyzed in two steps.

A5. Grigoris Antoniou:

One intended use of our logic is for formulation of specifications of controllers, which are to be compiled in a chain of the following form: (controllers in defeasible logic) -> (tables) -> microchips.

C5-1. Bob Kowalski:

(To Sandewall) There are plenty of other uses of nonmonotonic reasoning besides the ones you mentioned, in particular, for legal reasoning. (Agreement from McCarthy).

Q6. Graham White:

This approach seems to get quite complicated. What does it take to write down a formal description of a domain? and why did you choose this kind of logic in the first place?

A6. Grigoris Antoniou:

The original logic was not designed by us; it had been published before. Our goal is to try it out, and to relate it to other approaches in the area. We also see a need to develop systems for special cases to meet specific applications.

C6-1. Pat Hayes:

In defense of the proposed approach, it seems to me that we are never going to get our axioms bug-free, and one way of dealing with that is to use systems like this one.

C6-2. Graham White:

Still I wonder why it has to be so complicated.

C6-3. Pat Hayes:

That seems to be unavoidable.

C6-4. John McCarthy:

I don't think it's a question of bugs. (...)

C6-5. Pat Hayes:

Maybe "bugs" was the wrong word; I'm thinking of generalizations that seem plausible when you write them but which are in fact false. Rather than replacing them, it may be better to leave them where they are, but to be prepared to add other facts that cancel them out.

Q7. Bob Kowalski:

The presented article proposes a particular operational semantics. We now know that all of these kinds of systems (logic programming, etc) allow for multiple semantics... (End of the question not recorded).

A7. Grigoris Antoniou (2.2):

Indeed it is important to find other semantic accounts of the logic. We are particularly looking at argumentation-theoretic characterisations.

This on-line debate page is part of a discussion at recent workshop; similar pages are set up for each of the workshop articles. The discussion is organized by the area Reasoning about Actions and Change within the Electronic Transactions on Artificial Intelligence (ETAI).

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