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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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Cited by 49 (10 self)
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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.
Consistency and Constrained Optimisation for Conditional Preferences
"... TCPnets are an extension of CPnets which allow the expression of conditional relative importance of pairs of variables. In this paper it is shown that a simple logic of conditional preferences can be used to express TCPnet orders, as well as being able to represent much stronger statements of imp ..."
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Cited by 21 (7 self)
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TCPnets are an extension of CPnets which allow the expression of conditional relative importance of pairs of variables. In this paper it is shown that a simple logic of conditional preferences can be used to express TCPnet orders, as well as being able to represent much stronger statements of importance than TCPnets allow. The paper derives various sufficient conditions for a subset of the logical language to be consistent, and develops methods for finding a total order on outcomes which is consistent with the set of conditional preferences. This leads also to an approach to the problem of constrained optimisation.
Constraintbased preferential optimization
 in Proceedings of AAAI05
, 2005
"... We first show that the optimal and undominated outcomes of an unconstrained (and possibly cyclic) CPnet are the solutions of a set of hard constraints. We then propose a new algorithm for finding the optimal outcomes of a constrained CPnet which makes use of hard constraint solving. Unlike previou ..."
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Cited by 19 (5 self)
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We first show that the optimal and undominated outcomes of an unconstrained (and possibly cyclic) CPnet are the solutions of a set of hard constraints. We then propose a new algorithm for finding the optimal outcomes of a constrained CPnet which makes use of hard constraint solving. Unlike previous algorithms, this new algorithm works even with cyclic CPnets. In addition, the algorithm is not tied to CPnets, but can work with any preference formalism which produces a preorder over the outcomes. We also propose an approximation method which weakens the preference ordering induced by the CPnet, returning a larger set of outcomes, but provides a significant computational advantage. Finally, we describe a weighted constraint approach that allows to find good solutions even when optimals do not exist. 1
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.
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
The Complexity of Learning Separable ceteris paribus Preferences
"... We address the problem of learning preference relations on multiattribute (or combinatorial) domains. We do so by making a very simple hypothesis about the dependence structure between attributes that the preference relation enjoys, namely separability (no preferential dependencies between attribut ..."
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Cited by 7 (2 self)
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We address the problem of learning preference relations on multiattribute (or combinatorial) domains. We do so by making a very simple hypothesis about the dependence structure between attributes that the preference relation enjoys, namely separability (no preferential dependencies between attributes). Given a set of examples consisting of comparisons between alternatives, we want to output a separable CPnet, consisting of local preferences on each of the attributes, that fits the examples. We consider three forms of compatibility between a CPnet and a set of examples, and for each of them we give useful characterizations as well as complexity results. 1
Efficient Inference for Expressive Comparative Preference Languages
"... A fundamental task for reasoning with preferences is the following: given input preference information from a user, and outcomes α and β, should we infer that the user will prefer α to β? For CPnets and related comparative preference formalisms, inferring a preference of α over β using the standard ..."
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Cited by 7 (4 self)
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A fundamental task for reasoning with preferences is the following: given input preference information from a user, and outcomes α and β, should we infer that the user will prefer α to β? For CPnets and related comparative preference formalisms, inferring a preference of α over β using the standard definition of derived preference appears to be extremely hard, and has been proved to be PSPACEcomplete in general for CPnets. Such inference is also rather conservative, only making the assumption of transitivity. This paper defines a less conservative approach to inference which can be applied for very general forms of input. It is shown to be efficient for expressive comparative preference languages, allowing comparisons between arbitrary partial tuples (including complete assignments), and with the preferences being ceteris paribus or not. 1