Preference Orders on Families of Sets - When Can Impossibility Results Be Avoided?

Maly, Jan; Truszczyński, Mirosław; Woltran, Stefan

doi:10.24963/ijcai.2018/60

Cited by 3 publications

(5 citation statements)

References 2 publications

(7 reference statements)

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“…On the other hand, families of sets must have some internal structure to be succinctly represented. This internal structure may decrease the complexity of the problem, as is the case for the domain restrictions considered by Maly, Truszczyński, and Woltran (2018). We show -for a specific succinct representation that is well studied in the literature -that succinct representation can lead to a massive blow up in complexity.…”

Section: Introductionmentioning

confidence: 77%

“…Our results show that this can lead to a rise in complexity that may make recognizing strongly orderable families intractable even in applications that are not time-critical. On the other hand, Maly, Truszczyński, and Woltran (2018) showed that less expressive succinct representations can avoid this problem. Unfortunately, the representation considered in their paper is very limiting.…”

Section: Discussionmentioning

confidence: 99%

“…In this section, we investigate the effect of dropping the requirement that the lifted order should be total. It can be seen by carefully checking the proofs of Maly, Truszczyński, and Woltran (2018) that this has no effect for the special type of families considered in their paper if dominance and strict independence are considered. On the other hand, Maly and Woltran (2017) have shown that the order lifting problem becomes trivial if one only requires a preorder on the family of sets that satisfies dominance and independence.…”

Section: Incomplete Preferencesmentioning

confidence: 99%

“…Therefore, it is more important to know for a given family of sets if dominance and (strict) independence are compatible for any preference order the agents may report. 1 Following Maly, Truszczyński, and Woltran (2018) we call families of sets for which any possible order on the elements can be lifted to an order satisfying dominance and (strict) independence strongly orderable with respect to dominance and (strict) independence. Maly, Truszczyński, and Woltran (2018) studied this concept for a specific class of families of sets, namely for families of sets that can be represented as the family of all sets of vertices that induce a connected subgraphs in a given graph.…”

Section: Introductionmentioning

confidence: 99%

“…1 Following Maly, Truszczyński, and Woltran (2018) we call families of sets for which any possible order on the elements can be lifted to an order satisfying dominance and (strict) independence strongly orderable with respect to dominance and (strict) independence. Maly, Truszczyński, and Woltran (2018) studied this concept for a specific class of families of sets, namely for families of sets that can be represented as the family of all sets of vertices that induce a connected subgraphs in a given graph. One of their main results is a classification result that implies that strong orderability with respect to dominance and strict independence can be decided in polynomial time for families in this restricted class.…”

Section: Introductionmentioning

confidence: 99%

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Lifting Preferences over Alternatives to Preferences over Sets of Alternatives: The Complexity of Recognizing Desirable Families of Sets

Maly

2020

AAAI

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The problem of lifting a preference order on a set of objects to a preference order on a family of subsets of this set is a fundamental problem with a wide variety of applications in AI. The process is often guided by axioms postulating properties the lifted order should have. Well-known impossibility results by Kannai and Peleg and by Barberà and Pattanaik tell us that some desirable axioms – namely dominance and (strict) independence – are not jointly satisfiable for any linear order on the objects if all non-empty sets of objects are to be ordered. On the other hand, if not all non-empty sets of objects are to be ordered, the axioms are jointly satisfiable for all linear orders on the objects for some families of sets. Such families are very important for applications as they allow for the use of lifted orders, for example, in combinatorial voting. In this paper, we determine the computational complexity of recognizing such families. We show that it is Π2p-complete to decide for a given family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for all linear orders on the objects if the lifted order needs to be total. Furthermore, we show that the problem remains coNP-complete if the lifted order can be incomplete. Additionally, we show that the complexity of these problem can increase exponentially if the family of sets is not given explicitly but via a succinct domain restriction.

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Section: Introductionmentioning

confidence: 77%

Section: Discussionmentioning

confidence: 99%

Section: Incomplete Preferencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lifting Preferences over Alternatives to Preferences over Sets of Alternatives: The Complexity of Recognizing Desirable Families of Sets

Maly

2020

AAAI

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Ranking Sets of Defeasible Elements in Preferential Approaches to Structured Argumentation: Postulates, Relations, and Characterizations

Maly¹,

Wallner

2021

AAAI

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Preferences play a key role in computational argumentation in AI, as they reflect various notions of argument strength vital for the representation of argumentation. Within central formal approaches to structured argumentation, preferential approaches are applied by lifting preferences over defeasible elements to rankings over sets of defeasible elements, in order to be able to compare the relative strength of two arguments and their respective defeasible constituents. To overcome the current gap in the scientific landscape, we give in this paper a general study of the critical component of lifting operators in structured argumentation. We survey existing lifting operators scattered in the literature of argumentation theory, social choice, and utility theory, and show fundamental relations and properties of these operators. Extending existing works from argumentation and social choice, we propose a list of postulates for lifting operations, and give a complete picture of (non-)satisfaction for the considered operators. Based on our postulates, we present impossibility results, stating for which sets of postulates there is no hope of satisfaction, and for two main lifting operators presented in structured argumentation, Elitist and Democratic, we give a full characterization in terms of our postulates.

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An informant-based approach to argument strength in Defeasible Logic Programming

Cohen

Gottifredi

Tamargo

et al. 2021

AAC

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This work formalizes an informant-based structured argumentation approach in a multi-agent setting, where the knowledge base of an agent may include information provided by other agents, and each piece of knowledge comes attached with its informant. In that way, arguments are associated with the set of informants corresponding to the information they are built upon. Our approach proposes an informant-based notion of argument strength, where the strength of an argument is determined by the credibility of its informant agents. Moreover, we consider that the strength of an argument is not absolute, but it is relative to the resolution of the conflicts the argument is involved in. In other words, the strength of an argument may vary from one context to another, as it will be determined by comparison to its attacking arguments (respectively, the arguments it attacks). Finally, we equip agents with the means to express reasons for or against the consideration of any piece of information provided by a given informant agent. Consequently, we allow agents to argue about the arguments' strength through the construction of arguments that challenge (respectively, defeat) or are in favour of their informant agents.

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Preference Orders on Families of Sets - When Can Impossibility Results Be Avoided?

Cited by 3 publications

References 2 publications

Lifting Preferences over Alternatives to Preferences over Sets of Alternatives: The Complexity of Recognizing Desirable Families of Sets

Lifting Preferences over Alternatives to Preferences over Sets of Alternatives: The Complexity of Recognizing Desirable Families of Sets

Ranking Sets of Defeasible Elements in Preferential Approaches to Structured Argumentation: Postulates, Relations, and Characterizations

An informant-based approach to argument strength in Defeasible Logic Programming

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