Database preference queries—a possibilistic logic approach with symbolic priorities (original) (raw)

Erratum to: Database preference queries - a possibilistic logic approach with symbolic priorities

Annals of Mathematics and Artificial Intelligence, 2015

This note corrects a claim made in the above-mentioned paper about the exact representation of a conditional preference network by means of a possibilistic logic base with partially ordered symbolic weights. We provide a counterexample that shows that the possibilistic logic representation is indeed not always exact. This is the basis of a short discussion on the difficulty of obtaining an exact representation. This note corrects a claim made in [6] about the representation of Conditional Preference networks (CP-nets for short) [1] by means of a possibilistic logic base [2], as well as a similar claim in [7, 8]. A CP-net encodes a set of preference statements concerning the values of Boolean decision variables, conditioned on the values of other Boolean decision variables that influence the former. More formally, let V = {X 1 , • • • , X n } be a set of Boolean variables. We denote by Ast (S) the set of interpretations of variables of S (⊆ V). Definition 1 A CP-net N over V = {X 1 , • • • , X n } is a directed graph with nodes X 1 , • • • , X n , and there is a directed edge from X i to X j if the preference about the value X j depends on the value of X i. Each node X i ∈ V is associated with a conditional preference table CP T i that associates a strict preference (x i > ¬x i or ¬x i > x i

CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements

Journal of Artificial Intelligence Research, 2004

Information about user preferences plays a key role in automated decision making. In many domains it is desirable to assess such preferences in a qualitative rather than quantitative way. In this paper, we propose a qualitative graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably quite natural in many circumstances. We provide a formal semantics for this model, and describe how the structure of the network can be exploited in several inference tasks, such as determining whether one outcome dominates (is preferred to) another, ordering a set outcomes according to the preference relation, and constructing the best outcome subject to available evidence.

Conditional Preferences: A New Semantics for Database Queries

2008

Preference queries aim to retrieve from large databases those objects that better match user's requirements. Approaches proposed so far in the DB field for specifying preferences are limited when one needs to consider conditional, rather than absolute, preferences (e.g., I prefer driving by car in winter, and by motorbike in summer), which are common in context-aware applications. CP-nets are a powerful formalism for concisely representing such preferences, which has its roots in decision making problems. However, CP-nets, being based on a ceteris paribus (all else being equal) interpretation, are hardly applicable in complex DB scenarios. In this paper we introduce a new totalitarian (i.e., not ceteris paribus) semantics for CP-nets. We prove that our semantics is equivalent to ceteris paribus for complete acyclic CP-nets, whereas it avoids some counterintuitive effects of ceteris paribus when the CP-net is partially specified.

Database Preferences Queries - A Possibilistic Logic Approach with Symbolic Priorities

2008

The paper presents a new approach to database preferences queries, where preferences are represented in a possibilistic logic manner, using symbolic weights. The symbolic weights may be processed without assessing their precise value, which leaves the freedom for the user to not specify any priority among the preferences. The user may also enforce a (partial) ordering between them, if necessary. The approach can be related to the processing of fuzzy queries whose components are conditionally weighted in terms of importance. Here, importance levels are symbolically processed, and refinements of both Pareto ordering and minimum ordering are used. The representational power of the proposed setting is stressed, while the approach is compared with database Best operator-like methods and with the CP-net approach developed in artificial intelligence. The paper also provides a structured and rather broad overview of the different lines of research in the literature dealing with the handling of preferences in database queries.

On graphical modeling of preference and importance

2006

In recent years, CP-nets have emerged as a useful tool for supporting preference elicitation, reasoning, and representation. CP-nets capture and support reasoning with qualitative conditional preference statements, statements that are relatively natural for users to express. In this paper, we extend the CP-nets formalism to handle another class of very natural qualitative statements one often uses in expressing preferences in daily life -statements of relative importance of attributes. The resulting formalism, TCP-nets, maintains the spirit of CP-nets, in that it remains focused on using only simple and natural preference statements, uses the ceteris paribus semantics, and utilizes a graphical representation of this information to reason about its consistency and to perform, possibly constrained, optimization using it. The extra expressiveness it provides allows us to better model tradeoffs users would like to make, more faithfully representing their preferences.

Towards a formalization of the Linguistic Conditional Preference networks

HAL (Le Centre pour la Communication Scientifique Directe), 2012

In recent works, we have proposed a graphical model to represent linguistic preferences called LCP-nets. LCP-nets have been implemented and used in a specific use case of industrial engineering. In this paper, we consolidate this contribution in formalizing it through a set of notations and computation rules in order to guarantee its durability and its reusability to other multi-criteria decision contexts. The paper formalizes the LCP-net structure, semantics, and validity. It also formalizes the dominance testing and optimization queries (for a discretized version of the problem in this latter case), in the line of previous CP-nets models.

Reasoning with conditional ceteris paribus preference statements

Proceedings of the Fifteenth …, 1999

In many domains it is desirable to assess the preferences of users in a qualitative rather than quantitative way. Such representations of qualitative preference orderings form an important component of automated decision tools. We propose a graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably natural. We describe several search algorithms for dominance testing based on this representation; these algorithms are quite effective, especially in specific network topologies, such as chain- and tree-structured networks, as well as polytrees.

CP-nets: a tool for represent-ing and reasoning with conditional ceteris paribus state-ments

Journal of Artificial Intelligence Research, 2004

Information about user preferences plays a key role in automated decision making. In many domains it is desirable to assess such preferences in a qualitative rather than quantitative way. In this paper, we propose a qualitative graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably quite natural in many circumstances. We provide a formal semantics for this model, and describe how the structure of the network can be exploited in several inference tasks, such as determining whether one outcome dominates (is preferred to) another, ordering a set outcomes according to the preference relation, and constructing the best outcome subject to available evidence. abc 7 7 J J J J J Jā bc abc × × ' 'ā bc Õ Ȭ abc z z t t t t t t abc abc z z t t t t t t abc abc 7 7 K K K K K K

Lexicographic Preference Trees with Hard Constraints

Advances in Artificial Intelligence, 2019

The CP-net and the LP-tree are two fundamental graphical models for representing user's qualitative preferences. Constrained CPnets have been studied in the past in which a very expensive operation, called dominance testing, between outcomes is required. In this paper, we propose a recursive backtrack search algorithm that we call Search-LP to find the most preferable feasible outcome for an LP-tree extended to a set of hard constraints. Search-LP instantiates the variables with respect to a hierarchical order defined by the LP-tree. Since the LP-tree represents a total order over the outcomes, Search-LP simply returns the first feasible outcome without performing dominance testing. We prove that this returned outcome is preferable to every other feasible outcome.

On Programs with Linearly Ordered Multiple Preferences

Lecture Notes in Computer Science, 2004

The extended answer set semantics for logic programs allows for the defeat of rules to resolve contradictions. We propose a refinement of these semantics based on a preference relation on extended literals. This relation, a strict partial order, induces a partial order on extended answer sets. The preferred answer sets, i.e. those that are minimal w.r.t. the induced order, represent the solutions that best comply with the stated preference on extended literals. In a further extension, we propose linearly ordered programs that are equipped with a linear hierarchy of preference relations. The resulting formalism is rather expressive and essentially covers the polynomial hierarchy. E.g. the membership problem for a program with a hierarchy of height n is Σ P n+1 -complete. We illustrate an application of the approach by showing how it can easily express hierarchically structured weak constraints, i.e. a layering of "desirable" constraints, such that one tries to minimize the set of violated constraints on lower levels, regardless of the violation of constraints on higher levels.