The tastes of a user can be represented in a natural way by using qualitative preferences. In this paper, we explore how ontological knowledge expressed via existential rules can be combined with CP-theories to (i) represent qualitative preferences along with domain knowledge, and (ii) perform preference-based answering of conjunctive queries (CQs). We call these combinations ontological CP-theories (OCP-theories). We define skyline and k-rank answers to CQs based on the user's preferences encoded in an OCP-theory, and provide an algorithm for computing them. We also provide precise complexity (including data tractability) results for deciding consistency, dominance, and CQ skyline membership for OCP-theories.

The Conditional Preference Network (CP-net) graphically represents user's qualitative and conditional preference statements under the ceteris paribus interpretation. The constrained CP-net is an extension of the CP-net, to a set of constraints. The existing algorithms for solving the constrained CP-net require the expensive dominance testing operation. We propose three approaches to tackle this challenge. In our first solution, we alter the constrained CP-net by eliciting additional relative importance statements between variables, in order to have a total order over the outcomes. We call this new model, the constrained Relative Importance Network (constrained CPR-net). Consequently, We show that the Constrained CPR-net has one single optimal outcome (assuming the constrained CPR-net is consistent) that we can obtain without dominance testing. In our second solution, we extend the Lexicographic Preference Tree (LP-tree) to a set of constraints. Then, we propose a recursive backtrack search algorithm, that we call Search-LP, to find the most preferable outcome. We prove that the first feasible outcome returned by Search-LP (without dominance testing) is also preferable to any other feasible outcome. Finally, in our third solution, we preserve the semantics of the CP-net and propose a divide and conquer algorithm that compares outcomes according to dominance testing.

We propose a novel CP-Net based composition approach to qualitatively select an optimal set of consumers for an IaaS provider. The IaaS provider's and consumers' qualitative preferences are captured using CP-Nets. We propose a CP-Net composability model using the semantic congruence property of a qualitative composition. A greedy-based and a heuristic-based consumer selection approaches are proposed that effectively reduce the search space of candidate consumers in the composition. Experimental results prove the feasibility of the proposed composition approach.

This book provides a tutorial introduction to modern techniques for representing and reasoning about qualitative preferences with respect to a set of alternatives. The syntax and semantics of several languages for representing preference languages, including CP-nets, TCP-nets, CI-nets, and CP-theories, are reviewed. Some key problems in reasoning about preferences are introduced, including determining whether one alternative is preferred to another, or whether they are equivalent, with respect to a given set of preferences. These tasks can be reduced to model checking in temporal logic. Specifically, an induced preference graph that represents a given set of preferences can be efficiently encoded using a Kripke Structure for Computational Tree Logic (CTL).

The tastes of a user can be represented in a natural way by using qualitative preferences. In this paper, we explore how ontological knowledge expressed via existential rules can be combined with CP-theories to (i) represent qualitative preferences along with domain knowledge, and (ii) perform preference-based answering of conjunctive queries (CQs). We call these combinations ontological CP-theories (OCP-theories). We define skyline and k-rank answers to CQs based on the user’s preferences encoded in an OCP-theory, and provide an algorithm for computing them. We also provide precise complexity (including data tractability) results for deciding consistency, dominance, and CQ skyline membership for OCP-theories.

We introduce a novel qualitative preference representation language, preference trees , or P-trees . We show that the lan- guage is intuitive to specify preferences over combinatorial domains and it extends existing preference formalisms such as LP-trees , ASO-rules and possibilistic logic . We study rea- soning problems with P-trees and obtain computational com- plexity results.

We present a unified logical framework for representing and reasoning about both quantitative and qualitative preferences in fuzzy answer set programming [Saad, 2010; Saad, 2009; Subrahmanian, 1994], called fuzzy answer set optimization programs. The proposed framework is vital to allow defining quantitative preferences over the possible outcomes of qualitative preferences. We show the application of fuzzy answer set optimization programs to the course scheduling with fuzzy preferences problem described in [Saad, 2010]. To the best of our knowledge, this development is the first to consider a logical framework for reasoning about quantitative preferences, in general, and reasoning about both quantitative and qualitative preferences in particular.

We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming [Saad and Pontelli, 2006; Saad, 2006; Saad, 2007a], called probability answer set optimization programs. The proposed framework is vital to allow defining probability quantitative preferences over the possible outcomes of qualitative preferences. We show the application of probability answer set optimization programs to a variant of the well-known nurse restoring problem [Bard and Purnomo, 2005], called the nurse restoring with probability preferences problem. To the best of our knowledge, this development is the first to consider a logical framework for reasoning about probability quantitative preferences, in general, and reasoning about both probability quantitative and qualitative preferences in particular.