# Probabilistic Preference Logic Networks

*Thomas Lukasiewicz‚ Maria Vanina Martinez and Gerardo I. Simari*

### Abstract

Reasoning about an entity’s preferences (be it a user of an application, an individual targeted for marketing, or a group of people whose choices are of interest) has a long history in different areas of study. In this paper, we adopt the point of view that grows out of the intersection of databases and knowledge representation, where preferences are usually represented as strict partial orders over the set of tuples in a database or the consequences of a knowledge base. We introduce probabilistic preference logic networks (PPLNs), which flexibly combine such preferences with probabilistic uncertainty. Their applications are clear in domains such as the Social Semantic Web, where users often express preferences in an incomplete manner and through different means, many times in contradiction with each other. We show that the basic problems associated with reasoning with PPLNs (computing the probability of a world or a given query) are #P-hard, and then explore ways to make these computations tractable by: (i) leveraging results from order theory to obtain a polynomial-time randomized approximation scheme (FPRAS) under fixed-parameter assumptions; and (ii) studying a fragment of the language of PPLNs for which exact computations can be performed in fixed-parameter polynomial time.