Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion Trust-based belief change Emiliano Lorini ✶ Guifei Jiang ✶ , ✷ Laurent Perrussel ✶ ✶ IRIT – Université de Toulouse – France ✷ AIRG – University of Western Sydney – Penrith – Australia ECAI-2014 talk E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion Motivation (1/3) Communication among agents Agents are autonomous Two agents may react differently while facing new information Deciding to adapt Adapting belief Input � s❡♥❞❡r , ❝♦♥t❡♥t � Receiver adapts its belief with respect to its trust in the sender about the content . Should it trust the sender (about the content)? 1 Up to which ”trust degree” it should consider new 2 information? Our goal : Exhibiting the interplay between trust and belief. E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion Motivation (2/3) Typical Interplay between trust and belief change Impact of the trust degree If NY Times informs Bill that Luigi’s Burger is the best burger restaurant ( ❧❜ ) in NYC and Bill strongly trusts NYT about ❧❜ , then he should strongly believe ❧❜ Cumulative impact of the trust degree Jane trusts Trip Advisor, Hotels.com and Ebookers about Pine Hotel quality in a reasonable way. Trip Advisor, Hotels.com and Ebookers informs Jane that Pine Hotel-NYC is a bad hotel. Jane may strongly believe that Pine Hotel is a bad hotel. ⇒ Needs for a modular definition of the interplay E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion Motivation (3/3) How do we do that? How to represent ❜❡❧✐❡❢ ( ✐ , ❝♦♥t❡♥t , ❞❡❣r❡❡ ) and tr✉st ( ✐ , , ❥ , ❝♦♥t❡♥t , ❞❡❣r❡❡ ) (Static aspect) Epistemic Logic with a trust operator Extension with degree How to represent ✐♥❢♦r♠ ( ✐ , ❥ , ❝♦♥t❡♥t ) and r❡✈✐s❡ ( ❦ , ✐♥❢♦r♠ ( ✐ , ❥ , ❝♦♥t❡♥t )) (Dynamic aspect) Dynamic Epistemic Logic Iterated Belief Change a la Spohn. ⇒ DL-BT: Dynamic Logic of Graded Belief and Trust E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion Plan Motivation 1 DL-BT: Syntax 2 L-BT: Semantics 3 Structure Truth conditions DL-BT Semantics 4 Change Policies Additive Policy Compensatory Policy Axiomatics 5 L-BT: Proof theory DL-BT: Reduction axioms Change Policies: Reduction axioms Conclusion 6 E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion DL-BT: Syntax - Knowledge and Belief operators (1/2) ❑ ✐ ϕ : agent ✐ knows ϕ What is possible for agent ✐ ? ❇ ≥ α ϕ : agent ✐ believes that ϕ is true with strength at least α ✐ "What is possible" is structured as an epistemic state. Scale for beliefs: numerical scale ◆✉♠ = { ✵ , . . . , ♠❛① } Scale is finite and can be viewed as an encoding of a qualitative scale Example: ◆✉♠ = { ✵ , ✶ , ✷ , ✸ , ✹ , ✺ } s.t. ✵ stands for ’null’ and ✺ for ’very high’. Bill believes (at least weakly) that Luigi’s Burger is the best one in NYC: ¬ ❑ ❜✐❧❧ ❧✉✐❣✐ _ ❜❡st _ ❜✉r❣❡r ∧ ❇ ≥ ✶ ❜✐❧❧ ❧✉✐❣✐ _ ❜❡st _ ❜✉r❣❡r E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion DL-BT: Syntax - Knowledge and Belief operators (2/2) Knowledge Shortcut � ❑ ✐ ϕ = ❞❡❢ ¬ ❑ ✐ ¬ ϕ Belief shortcut ❇ ✐ ϕ = ❞❡❢ ❇ ≥ ✶ � ❇ ✐ ϕ = ❞❡❢ ¬ ❇ ✐ ¬ ϕ ϕ ✐ ϕ ∧ ¬ ❇ ≥ ( α + ✶ ) ✐ ϕ = ❞❡❢ ❇ ≥ α ❇ α ❯ ✐ ϕ = ❞❡❢ ¬ ❇ ✐ ϕ ∧ ¬ ❇ ✐ ¬ ϕ ϕ ✐ ✐ ϕ = ❞❡❢ ❇ ≥ ♠❛① ❇ ♠❛① ❇ ✵ ✐ ϕ = ❞❡❢ ¬ ❇ ✐ ϕ ϕ ✐ ✐ Example: Bill believes that Luigi’s Burger is the best one in NYC: ❇ ❜✐❧❧ ❧✉✐❣✐ _ ❜❡st _ ❜✉r❣❡r Bill only weakly believes that Luigi is the best one: ❇ ✶ ❜✐❧❧ ❧✉✐❣✐ _ ❜❡st _ ❜✉r❣❡r E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion DL-BT: Syntax - Trust Operator ❚ α ✐ , ❥ ϕ : agent ✐ trusts agent ❥ ’s judgement on formula ϕ with strength α . α � ✵ 1 Trust degree is exactly α (and not a lower bound) 2 Scale is shared with the belief scale 3 Shortcut � ❚ α ❚ ✐ , ❥ ϕ = ❞❡❢ ✐ , ❥ ϕ α ∈ ◆✉♠ \{ ✵ } Example: Bill strongly trusts NYT about Luigi: ❚ ✹ ❜✐❧❧ , ♥②t ❧✉✐❣✐ _ ❜❡st _ ❜✉r❣❡r L-BT: Logic of Graded Belief and Trust E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion DL-BT: Syntax - Revision Operator Interplay between trust and change may be specific to each agent: ❢ is a policy change function. [ ∗ ❢ ✐ ψ ] ϕ : after agent ✐ has publicly announced that ψ is true and each agent ❥ has revised her beliefs according to the trust-based belief change policy ❢ ( ❥ ) , ϕ is true. Example: Bill believes that Luigi is the best after NYT announces it (w.r.t. some ❢ ( ❜✐❧❧ ) ): [ ∗ ❢ ♥②t ❧✉✐❣✐ _ ❜❡st _ ❜✉r❣❡r ] ❇ ❜✐❧❧ ❧✉✐❣✐ _ ❜❡st _ ❜✉r❣❡r DL-BT: L-BT logic + revision operator E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion L-BT: Semantics - Structure (1/3) Kripke semantics For each agent ✐ : possible states: equivalence relation E ✐ Example: E ✐ ( ✇ ✵ ) = { ✇ ✵ , ✇ ✶ , ✇ ✷ , ✇ ✸ , ✇ ✹ , ✇ ✺ } ranking of the states: κ function 0 is the best value κ ( ✇ , ✐ ) : how exceptional is ✇ for agent ✐ 2 ✇ ✸ , ✇ ✹ , ✇ ✺ Example: 1 ✇ ✷ 0 ✇ ✵ , ✇ ✶ for any state and agent, there is always a possible state with a 0 value (consistency). E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion L-BT: Semantics - Structure (2/3) Neighbourhood semantics for trust Non normal operator for handling trust about contradicting statements. For each agent ✐ and state ✇ : ❥ -trustable states: function N ✐ , ❥ ( ✇ , α ) Example: N ✐ , ❥ ( ✇ ✵ , ✶ ) = {{ ✇ ✶ }} N ✐ , ❥ ( ✇ ✵ , ✷ ) = {{ ✇ ✸ , ✇ ✹ }} N ✐ , ❥ ( ✇ ✵ , ✸ ) = {{ ✇ ✵ , ✇ ✷ }{ ✇ ✵ , ✇ ✺ }} constraint on N ✐ , ❥ no two states with different degrees two equivalent possible states must lead to the trustable states (and values) trustable states must be possible states E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion L-BT: Semantics - Structure (3/3) Valuations V on each state To sum up, a model ▼ = ( ❲ , {E ✐ } ✐ ∈ ❆❣t , κ , {N ✐ , ❥ } ✐ , ❥ ∈ ❆❣t , V ) Exceptionality degree of a formula ϕ (w.r.t. some ✇ and ✐ ): κ ✇ , ✐ ( ϕ ) = ♠✐♥ ✈ ∈� ϕ � ✇ , ✐ κ ( ✈ , ✐ ) if � ϕ � ✇ , ✐ � = ∅ κ ✇ , ✐ ( ϕ ) = ♠❛① if � ϕ � ✇ , ✐ = ∅ E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion L-BT: Semantics - Truth conditions Truth conditions are defined with respect to some model ▼ and a state ✇ . ▼ , ✇ | = ❑ ✐ ϕ iff ∀ ✈ ∈ E ✐ ( ✇ ) : ▼ , ✈ | = ϕ = ❇ ≥ α ▼ , ✇ | ϕ iff κ ✇ , ✐ ( ¬ ϕ ) ≥ α ✐ = ❚ α ▼ , ✇ | ✐ , ❥ ϕ iff � ϕ � ▼ ∈ N ✐ , ❥ ( ✇ , α ) E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
Motivation DL-BT: Syntax L-BT: Semantics DL-BT Semantics Axiomatics Conclusion DL-BT: - Embedding policies Policy: how to change degrees ( κ values). Input: an L-BT model ▼ = ( ❲ , {E ✐ } ✐ ∈ ❆❣t , κ , {N ✐ , ❥ } ✐ , ❥ ∈ ❆❣t , V ) Function ❢ maps a policy to each agent. Output: new degrees κ ∗ ❢ ✐ ϕ ( ✇ , ❥ ) : κ values for agent ❥ revised w.r.t. ▼ , ❢ and initial announcement ϕ by ✐ . ... and a new model ✐ ϕ = ( ❲ , {E ✐ } ✐ ∈ ❆❣t , κ ∗ ❢ ▼ ∗ ❢ ✐ ϕ , {N ✐ , ❥ } ✐ , ❥ ∈ ❆❣t , V ) Semantics of the revision ✐ ϕ ] ψ iff ▼ ∗ ❢ = [ ∗ ❢ ✐ ϕ , ✇ | ▼ , ✇ | = ψ E. Lorini, G. Jiang, L. Perrussel Trust-based belief change
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