Defeasibility in Answer Set Programs with Defaults and Argumentation Rules

Tracking #: 547-1750

Hui Wan
Michael Kifer
Benjamin Grosof

Responsible editor: 
Thomas Lukasiewicz

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Defeasible reasoning has been studied extensively in the last two decades and many different and dissimilar approaches are currently on the table. This multitude of ideas has made the field hard to navigate and the different techniques hard to compare. Our earlier work on Logic Programming with Defaults and Argumentation Theories (LPDA) introduced a degree of unification into the approaches that rely on the well-founded semantics. The present work takes this idea further and introduces ASPDA (Answer Set Programs via Argumentation Rules) — a unifying framework for defeasibility of disjunctive logic programs under the Answer Set Programming (ASP). Since the well-founded and the answer set semantics underlie almost all existing approaches to defeasible reasoning in Logic Programming, LPDA and ASPDA together can closely approximate most of those approaches. In addition to ASPDA, we obtained a number of interesting and non-trivial results. First, we show that ASPDA is reducible to ordinary ASP programs. Second, we study reducibility of ASPDA to the non-disjunctive case and show that head-cycle-free ASPDA programs reduce to the non-disjunctive case — similarly to head-cycle-free ASP programs, but through a more complex transformation.We also shed light on the relationship between ASPDA and some of the earlier theories such as Defeasible Logic and LPDA.
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Review #1
By Guido Governatori submitted on 22/Dec/2013
Minor Revision
Review Comment:

The current version is an improvement on the previous one, and as I have always said it contains interesting results worth of being published. The authors did some changes, but I feel that something more is needed. One of those changes was replace the terms "to simulate" and "to capture" with "to closely approximate", claiming that the first two are ambiguous and the last is not. Actually, I'm not sure about this. Personally I have a good understanding of what "to simulate" or "to capture" mean, but I have no idea of what "to closely approximate" means. I would suggest to closely approximate their intended meaning with the expression "based on the intuition of the logic of [1] under the stable semantics" or "inspired by the logic of [1] under the stable semantics". As I said before I would consider the well-founded semantics of Maher Governatori 1999, for which there is a correspondence result (and not only when there are no loops in the dependency graph).

I think the authors did a good job in revising examples 2, 3 and 4. However, I think a better discussion of example 5 is needed; personally I don't found the intuition you included very convincing. I think you have to discuss the option where a cycle in the #overrides relation is an inconsistency (suppose that the meaning of #overrides is how much one is confident in a rule; then your example says that "I'm more confident in rule @r1 than rule @r2", and "I'm more confident in rule @r2 than rule @r1").

On naf, on page 13, second column item 1, you wrote: "AT^{DL} does not support naf or disjunction in rule heads;". First of all I would invert the disjunction, i.e., "it does not support disjunction in rule head or naf"
What does it mean that "it does not support naf". Consider an axiomatisation of propositional logic defined on implication and negation. It does not use disjunction or conjunction. Are disjunction and conjunction not supported?

In Section2 (at the end of the section) you mention that "existing logic programming approaches to defeasible reasoning cannot handle the above situation". What about plausible logic (reference [5], what about [9], also what about the approaches with ordered disjunction). Also, in Example 2, you mention that there is a workaround for AT^{DL}.

author = {Gerhard Brewka and
Ilkka Niemel{\"a} and
Tommi Syrj{\"a}nen},
title = {Logic Programs with Ordered Disjunction},
journal = {Computational Intelligence},
volume = {20},
number = {2},
year = {2004},
pages = {335-357},
ee = {},
bibsource = {DBLP,}

Page 4, column 1, definition 3: Here you repeat that "Sometimes we will omit tags when they are immaterial", you wrote it just before Definition 2.

Definition 7, last paragraph, you cannot use a tag like @r to refer to a rule, since as you wrote several times it is not rule identifier.