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The Computational Complexity of Dominance and Consistency in CPNets
"... We investigate the computational complexity of testing dominance and consistency in CPnets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CPnet is acyclic. However, there are preferences of interest that define cyclic depend ..."
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We investigate the computational complexity of testing dominance and consistency in CPnets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CPnet is acyclic. However, there are preferences of interest that define cyclic dependency graphs; these are modeled with general CPnets. In our main results, we show here that both dominance and consistency for general CPnets are PSPACEcomplete. We then consider the concept of strong dominance, dominance equivalence and dominance incomparability, and several notions of optimality, and identify the complexity of the corresponding decision problems. The reductions used in the proofs are from STRIPS planning, and thus reinforce the earlier established connections between both areas.
Preference Handling  An Introductory Tutorial
"... We present a tutorial introduction to the area of preference handling – one of the core issues in the design of any system that automates or supports decision making. The main goal of this tutorial is to provide a framework, or perspective, within which current work on preference handling – represen ..."
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Cited by 23 (0 self)
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We present a tutorial introduction to the area of preference handling – one of the core issues in the design of any system that automates or supports decision making. The main goal of this tutorial is to provide a framework, or perspective, within which current work on preference handling – representation, reasoning, and elicitation – can be understood. Our intention is not to provide a technical description of the diverse methods used, but rather, to provide a general perspective on the problem and its varied solutions and to highlight central ideas and techniques.
Conditional Importance Networks: A Graphical Language for Representing Ordinal, Monotonic Preferences over Sets of Goods
"... While there are several languages for representing combinatorial preferences over sets of alternatives, none of these are wellsuited to the representation of ordinal preferences over sets of goods (which are typically required to be monotonic). We propose such a language, taking inspiration from pr ..."
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Cited by 15 (6 self)
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While there are several languages for representing combinatorial preferences over sets of alternatives, none of these are wellsuited to the representation of ordinal preferences over sets of goods (which are typically required to be monotonic). We propose such a language, taking inspiration from previous work on graphical languages for preference representation, specifically CPnets, and introduce conditional importance networks (CInets). A CInet includes statements of the form “if I have a set A of goods, and I do not have any of the goods from some other set B, then I prefer the set of goods C over the set of goods D. ” We investigate expressivity and complexity issues for CInets. Then we show that CInets are wellsuited to the description of fair division problems. 1
From Preference Logics to Preference Languages, and Back
"... Preference logics and AI preference representation languages are both concerned with reasoning about preferences on combinatorial domains, yet so far these two streams of research have had little interaction. This paper contributes to the bridging of these areas. We start by constructing a “prototyp ..."
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Cited by 15 (2 self)
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Preference logics and AI preference representation languages are both concerned with reasoning about preferences on combinatorial domains, yet so far these two streams of research have had little interaction. This paper contributes to the bridging of these areas. We start by constructing a “prototypical” preference logic, which combines features of existing preference logics, and then we show that many wellknown preference languages, such as CPnets and its extensions, are natural fragments of it. After establishing useful characterizations of dominance and consistency in our logic, we study the complexity of satisfiability in the general case as well as for meaningful fragments, and we study the expressive power as well as the relative succinctness of some of these fragments. 1.
Preference queries over sets
 In ICDE
, 2011
"... Abstract—We propose a “logic + SQL ” framework for set preferences. Candidate best sets are represented using profiles consisting of scalar features. This reduces set preferences to tuple preferences over set profiles. We propose two optimization techniques: superpreference and Mrelation. Superpref ..."
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Cited by 12 (1 self)
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Abstract—We propose a “logic + SQL ” framework for set preferences. Candidate best sets are represented using profiles consisting of scalar features. This reduces set preferences to tuple preferences over set profiles. We propose two optimization techniques: superpreference and Mrelation. Superpreference targets dominated profiles. It reduces the input size by filtering out tuples not belonging to any best ksubset. Mrelation targets repeated profiles. It consolidates tuples that are exchangeable with regard to the given set preference, and therefore avoids redundant computation of the same profile. We show the results of an experimental study that demonstrates the efficacy of the optimizations. I.
Graphically structured valuefunction compilation
 Artificial Intelligence
"... Classical work on eliciting and representing preferences over multiattribute alternatives has attempted to recognize conditions under which value functions take on particularly simple and compact form, making their elicitation much easier. In this paper we consider preferences over discrete domains ..."
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Cited by 11 (2 self)
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Classical work on eliciting and representing preferences over multiattribute alternatives has attempted to recognize conditions under which value functions take on particularly simple and compact form, making their elicitation much easier. In this paper we consider preferences over discrete domains, and show that for a certain class of simple and intuitive qualitative preference statements, one can always generate compact value functions consistent with these statements. These value functions maintain the independence structure implicit in the original statements. For discrete domains, these representation theorems are much more general than previous results. However, we also show that it is not always possible to maintain this compact structure if we add explicit ordering constraints among the available outcomes. Brafman, & Domshlak 1.
Ceteris Paribus Preference Elicitation with Predictive Guarantees
"... CPnetworks have been proposed as a simple and intuitive graphical tool for representing conditional ceteris paribus preference statements over the values of a set of variables. While the problem of reasoning with CPnetworks has been receiving some attention, there are very few works that address t ..."
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Cited by 9 (0 self)
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CPnetworks have been proposed as a simple and intuitive graphical tool for representing conditional ceteris paribus preference statements over the values of a set of variables. While the problem of reasoning with CPnetworks has been receiving some attention, there are very few works that address the problem of learning CPnetworks. In this work we investigate the task of learning CPnetworks, given access to a set of pairwise comparisons. We first prove that the learning problem is intractable, even under several simplifying assumptions. We then present an algorithm that, under certain assumptions about the observed pairwise comparisons, identifies a CPnetwork that entails these comparisons. We finally show that the proposed algorithm is a PAClearner, and, thus, that the CPnetworks it induces accurately predict the user’s preferences on previously unseen situations. 1
Dominance Testing via Model Checking
"... Dominance testing, the problem of determining whether an outcome is preferred over another, is of fundamental importance in many applications. Hence, there is a need for algorithms and tools for dominance testing. CPnets and TCPnets are some of the widely studied languages for representing and rea ..."
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Cited by 9 (3 self)
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Dominance testing, the problem of determining whether an outcome is preferred over another, is of fundamental importance in many applications. Hence, there is a need for algorithms and tools for dominance testing. CPnets and TCPnets are some of the widely studied languages for representing and reasoning with preferences. We reduce dominance testing in TCPnets to reachability analysis in a graph of outcomes. We provide an encoding of TCPnets in the form of a Kripke structure for CTL. We show how to compute dominance using NuSMV, a model checker for CTL. We present results of experiments that demonstrate the feasibility of our approach to dominance testing.
LexicographicallyOrdered Constraint Satisfaction Problems
, 2009
"... We describe a simple CSP formalism for handling multiattribute preference problems with hard constraints, one that combines hard constraints and preferences so the two are easily distinguished conceptually and for purposes of problem solving. Preferences are represented as a lexicographic order ov ..."
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Cited by 7 (3 self)
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We describe a simple CSP formalism for handling multiattribute preference problems with hard constraints, one that combines hard constraints and preferences so the two are easily distinguished conceptually and for purposes of problem solving. Preferences are represented as a lexicographic order over complete assignments based on variable importance and rankings of values in each domain. Feasibility constraints are treated in the usual manner. Since the preference representation is ordinal in character, these problems can be solved with algorithms that do not require evaluations to be represented explicitly. This includes ordinary CSP algorithms, although these cannot stop searching until all solutions have been checked, with the important exception of heuristics that follow the preference order (lexical variable and value ordering). We describe relations between lexicographic CSPs and more general soft constraint formalisms and show how a full lexicographic ordering can be expressed in the latter. We discuss relations with (T)CPnets, highlighting the advantages of the present formulation, and we discuss the use of lexicographic ordering in multiobjective optimisation. We also