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An analytic logic of aggregation Patrick Girard and Jeremy Seligman - - PowerPoint PPT Presentation
An analytic logic of aggregation Patrick Girard and Jeremy Seligman - - PowerPoint PPT Presentation
An analytic logic of aggregation Patrick Girard and Jeremy Seligman University of Auckland ICLA 2009, Chennai 9 January 2009 Hierarchy Agreement Subordination Basic Preference Logic Start with a basic preference order (reflexive and
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Hierarchy
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Agreement
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Subordination
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Basic Preference Logic
- Start with a basic preference order
≤ (reflexive and transitive) over a set of objects (or states):
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Basic Preference Logic
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Preference Logic
- Are stars preferred to squares?
- Is red preferred to yellow?
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Preference Logic
- Existential modality:
– –
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Preference Logic
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Aggregation Logic
- Language:
- Models:
– – – –
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Semantics
- – There is a state at least as good as the current
state where holds.
- – There is a state strictly better than the current
state where holds.
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Aggregation Logic
1,2 1 2 1,2
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Preference Logic
1,2 1,2 1 2
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Which aggregation operators can we represent?
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Lexicographic (re)ordering
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Can we get rid of hierarchies?
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Arrow's Theorem
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Axiomatization
- Basic Hybrid logic
- Preference axioms,
- Aggregation axioms
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