Abstract
We are aiming at a semantics of logic programs with preferences defined on rules, which always selects a preferred answer set, if there is a non-empty set of (standard) answer sets of the given program.
It is shown in a seminal paper by Brewka and Eiter that the goal mentioned above is incompatible with their second principle and it is not satisfied in their semantics of prioritized logic programs. Similarly, also according to other established semantics, based on a prescriptive approach, there are programs with standard answer sets, but without preferred answer sets.
According to the standard prescriptive approach no rule can be fired before a more preferred rule, unless the more preferred rule is blocked. This is a rather imperative approach, in its spirit. According to our background intuition, rules can be blocked by more preferred rules, but the rules which are not blocked are handled in a more declarative style, independent on the given preference relation on the rules.
An argumentation framework (different from Dung’s framework) is proposed in this paper. Some argumentation structures are assigned to the rules of a given program. Other argumentation structures are derived using a set of derivation rules. Some of the derived argumentation structures correspond to answer sets. An attack relation on derivations of argumentation structures is defined. Preferred answer sets correspond to complete argumentation structures, which are not blocked by other complete argumentation structures.
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Notes
- 1.
Our intuitions connected to the notion of argumentation structure and also the used constructions are different from Dung’s arguments or from arguments of [8]. This paper does not present a contribution to argumentation theory.
- 2.
\(P^{+}\) is treated as definite logic program, i.e., each objective literal of the form \(\lnot A\), where \(A \in At \), is considered as a new atom.
- 3.
\(Cn_{\ll _P}(W)\) could be defined as \(T_P^\omega (W)\) and \(L \ll _P W\) as \(L \in T_P^\omega (W)\).
- 4.
This notation does not refer to \(P\) explicitly, but the condition \(Y \subseteq Cn _{\ll _{P \cup Z}}(X)\) relates a dependency structure to \(P\). Moreover, we will use only a kind of dependency structures, called argumentation structures, derived from a given program \(P\).
- 5.
If we abstract from the order of argumentation structures in the derivation. This does not influence the attack relation between derivations.
- 6.
Observe that the only derived complete argumentation structure is \(\langle \{ b \}\hookleftarrow \{ not \;a, not \;c \} \rangle \). Hence, \(\{ b \}\) is a preferred answer set in our framework.
- 7.
Of course, there are different possible ways how to specify the notion of defeat. A definition of defeated generating sets of rules can be obtained in a straightforward way from the notion of defeat presented in this paper.
References
Brewka, G., Eiter, T.: Preferred answer sets for extended logic programs. Artif. Intell. 109(1–2), 297–356 (1999)
Delgrande, J., Schaub, T., Tompits, H.: A framework for compiling preferences in logic programs. Theory Pract. Logic Program. 3(2), 129–187 (2003)
Delgrande, J., Schaub, T.: Expressing preferences in default logic. Artif. Intell. 123(1–2), 41–87 (2000)
Delgrande, J., Schaub, T., Tompits, H., Wang, K.: A classification and survey of preference handling approaches in nonmonotonic reasoning. Comput. Intell. 20(2), 308–334 (2004)
Dimopoulos, Y., Torres, A.: Graph theoretical structures in logic programs and default theories. Theoret. Comput. Sci. 170(1–2), 209–244 (1996)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 321–357 (1995)
Gabaldon, A.: A selective semantics for logic programs with preferences. In: Proceedings of the International Workshop on Nonmonotonic Reasoning, Action and Change (NRAC 11), Barcelona, Spain (2011)
García, A.J., Simari, G.R.: Defeasible logic programming: an argumentative approach. Theory Pract. Logic Program. 4(1–2), 95–138 (2004)
Sakama, C., Inoue, K.: Prioritized logic programming and its application to commonsense reasoning. Artif. Intell. 3(1–2), 185–222 (2000)
Schaub, T., Wang, K.: A comparative study of logic programs with preference. In: IJCAI 2001, pp. 597–602 (2001)
Šefránek, J.: Rethinking semantics of dynamic logic programs. In: Proceedings of the Workshop NMR (2006)
Šefránek, J.: Preferred answer sets supported by arguments. In: Proceedings of the Workshop NMR (2008)
Šefránek, J., Šimko, A.: Warranted derivation of preferred answer sets. In: Proceedings of WLP (2011)
Šimko, A.: Preferred answer sets - banned generating set. In: Proceedings of the Student Conference, Bratislava 2011, Faculty of Mathematics, Physics and Informatics, Comenius University, pp. 326–333 (2011)
Šimko, A.: Selection of a preferred answer sets as a decision between generating sets. In: 6th Workshop on Intelligent and Knowledge Oriented Technologies, pp. 51–56 (2011)
Šimko, A.: Accepting the natural order of rules in a logic program with preferences. In: Proceedings of the Doctoral Consortium at ICLP 2011 (2011)
Wakaki, T.: Preference-based argumentation handling dynamic preferences built on prioritized logic programming. In: Kinny, D., Hsu, J.-I., Governatori, G., Ghose, A.K. (eds.) PRIMA 2011. LNCS, vol. 7047, pp. 336–348. Springer, Heidelberg (2011)
Wang, K., Zhou, L.-Z., Lin, F.: Alternating fixpoint theory for logic programs with priority. In: Palamidessi, C., et al. (eds.) CL 2000. LNCS (LNAI), vol. 1861, p. 164. Springer, Heidelberg (2000)
Acknowledgments
We are grateful to anonymous referees for careful reading, for very valuable, detailed and helpful comments and proposals. This paper was supported by the grants 1/0689/10 and 1/1333/12 of VEGA.
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Šefránek, J., Šimko, A. (2013). A Descriptive Approach to Preferred Answer Sets. In: Tompits, H., et al. Applications of Declarative Programming and Knowledge Management. INAP WLP 2011 2011. Lecture Notes in Computer Science(), vol 7773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41524-1_11
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