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Multi-Attribute Preference Logic. Koen V. Hindriks, Wietske Visser, Catholijn M. Jonker. Overview. Motivating Context Informal Example Objectives Intuitions Multi-Attribute Preference Logic. Making the machine a negotiation partner. Pocket Negotiator project

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Multi attribute preference logic

Multi-Attribute Preference Logic

Koen V. Hindriks, Wietske Visser, Catholijn M. Jonker


Overview
Overview

  • Motivating Context

  • Informal Example

  • Objectives

  • Intuitions

  • Multi-Attribute Preference Logic


Making the machine a negotiation partner
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


Automated negotiating agents competition 2011 @ aamas
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


Informal example problem
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.


Objectives
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


Example cont d
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.


Need for ordering strategies
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?


Ordering strategy lexmin
Ordering Strategy: Lexmin (#)

consider the most important properties in order

house1 > house2 > house3

Other orderings: best-out, discrimin, …


Semantic intuitions for mpl
Semantic Intuitions for MPL

  • As usual, properties can be represented by sets of worlds

  • We also represent objects as (sets of) world(s)


Multi attribute preference logic mpl
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


Language of mpl
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)


Expressing ordering strategies in mpl
Expressing Ordering Strategiesin MPL

  • Read pref(i,j) as object i is preferred over j

  • Definitions for τ, κ, # orderings


Conclusion
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