Multi-Attribute Preference Logic

1. Multi-Attribute Preference Logic Koen V. Hindriks, Wietske Visser, Catholijn M. Jonker

2. Overview • Motivating Context • Informal Example • Objectives • Intuitions • Multi-Attribute Preference Logic

3. Making the machinea negotiation partner • Pocket Negotiator project • Synergy between man and machine • Provides support for negotiating • Various Components: • Negotiating strategy • Preference elicitation • Preference representation • Emotions in negotiation • We are interested in: Qualitative Preference Representation and Reasoning

4. Automated Negotiating Agents Competition 2011 @ AAMAS GENIUS Environment http://mmi.tudelft.nl/negotiation GENIUS = Java-Based Negotiation Environment http://www.anac2011.com Deadline for agent submissions January 31st, 2011

5. Informal example (problem) Suppose we want to buy a house. Also suppose we’re considering three houses (objects): • house1, house2 and house3. The properties that are important (in the order presented): • we can afford the house (affordable), • it is close to our work (closeToWork), and • it is large (large). Now, suppose we have an assignment of houses to properties. We’d like to figure out which house is most preferred.

6. Objectives • Provide a logical framework for reasoning with multi-attribute preferences. • Capture and formalize different preference ordering strategies • Built on and extend existing work on preference logics

7. Example (cont’d) Start with a set of properties of objects… Observation: … and note that preferences for these objects are commonly derived from ranked sets of properties (attributes) associated with these objects.

8. Need for Ordering Strategies • It seems clear that we would prefer house1 over the other two • But what about the relative preference of house2 and house3?

9. Ordering Strategy: Lexmin (#) consider the most important properties in order house1 > house2 > house3 Other orderings: best-out, discrimin, …

10. Semantic Intuitions for MPL • As usual, properties can be represented by sets of worlds • We also represent objects as (sets of) world(s)

11. Multi-Attribute Preference Logic (MPL) • Key to a logic of multi-attribute preferences is the representation of property rankings • A logic for qualitative multi-attribute preferences • Facilitates reasoning with property rankings and to formalize associated strategies for deriving object preferences from such rankings

12. Language of MPL • Propositional, modal logic • Special propositions i that can be used to refer to sets of worlds (=objects; compare with hybrid logic) • Operator represents that φ is true in all worlds preferred over the current one • Operator represents that φ is true in all words not equally preferred to the current one • Operator represents the usual universal operator in ML • operators extend preference logic of Girard (2008)

13. Expressing Ordering Strategiesin MPL • Read pref(i,j) as object i is preferred over j • Definitions for τ, κ, # orderings

14. Conclusion • Introduced modal logic for expressing ordering strategies for multi-attribute preferences • Showed that other preference formalisms (ranked knowledge bases) can be translated into multi-attribute preference logic • Future work: • Partial orderings • Currently logic supports binary preferences • Axiomatization