On the Revision of Action Laws: an Algorithmic Approach
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On the Revision of Action Laws: an Algorithmic Approach

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Work presented at the IJCAI'09 workshop on Nonmonotonic Reasoning, Action and Change (NRAC'09).

Work presented at the IJCAI'09 workshop on Nonmonotonic Reasoning, Action and Change (NRAC'09).

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    On the Revision of Action Laws: an Algorithmic Approach On the Revision of Action Laws: an Algorithmic Approach Presentation Transcript

    • On the Revision of Action Laws An Algorithmic Approach Ivan Jos´ Varzinczak e Knowledge Systems Group Meraka Institute CSIR Pretoria, South Africa NRAC’2009 Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 1 / 25
    • Motivation Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation Knowledge Base ‘A coffee is a hot drink’ ‘With a token I can buy coffee’ ‘Without a token I cannot buy’ ‘After buying I have a hot drink’ ... Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, t, ¬c, ¬h Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation Observations ‘Only coffee on the machine’ ‘After buying, I lose my token’ ‘Coffee is for free’ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation Observations ‘Only coffee on the machine’ ‘After buying, I lose my token’ ‘Coffee is for free’ Need for change the laws about the behavior of actions Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, t, ¬c, ¬h Need for change the laws about the behavior of actions Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation ¬k, ¬t, c, h k, ¬t, c, h b b k, t, c, h b b k, t, ¬c, ¬h Need for change the laws about the behavior of actions Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, t, ¬c, ¬h Need for change the laws about the behavior of actions Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation k, ¬t, c, h b b k, t, c, h k, t, ¬c, h b k, t, ¬c, ¬h Need for change the laws about the behavior of actions Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, t, ¬c, ¬h Need for change the laws about the behavior of actions Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Motivation b k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, t, ¬c, ¬h Need for change the laws about the behavior of actions Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
    • Outline Preliminaries Action Theories in Multimodal Logic Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 3 / 25
    • Outline Preliminaries Action Theories in Multimodal Logic Revision of Laws Semantics of Revision Algorithms Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 3 / 25
    • Outline Preliminaries Action Theories in Multimodal Logic Revision of Laws Semantics of Revision Algorithms Conclusion Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 3 / 25
    • Preliminaries Action Theories in Multimodal Logic Outline Preliminaries Action Theories in Multimodal Logic Revision of Laws Semantics of Revision Algorithms Conclusion Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 4 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Multimodal Logic ◮ Well defined semantics ◮ Expressive ◮ Decidable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 5 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Multimodal Logic ◮ Well defined semantics ◮ Possible worlds models ◮ Expressive ◮ Decidable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 5 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Multimodal Logic ◮ Well defined semantics ◮ Possible worlds models ◮ Expressive ◮ Actions, state constraints, nondeterminism ◮ Decidable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 5 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Multimodal Logic ◮ Well defined semantics ◮ Possible worlds models ◮ Expressive ◮ Actions, state constraints, nondeterminism ◮ Decidable ◮ exptime-complete, though Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 5 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Multimodal Logic ◮ Well defined semantics ◮ Possible worlds models ◮ Expressive ◮ Actions, state constraints, nondeterminism ◮ Decidable ◮ exptime-complete, though But of course ◮ I have nothing against Situation Calculus, Fluent Calculus, . . . Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 5 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Possible worlds semantics: Transition Systems M = W , R ◮ W : possible worlds ◮ R : accessibility relation a1 p1 , ¬p2 p1 , p2 a2 M : a2 a1 ¬p1 , p2 Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 6 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Describing Laws In RAA: 3 types of laws ◮ Static Laws: ϕ ◮ Ex.: p1 ∨ p2 Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 7 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Describing Laws In RAA: 3 types of laws ◮ Static Laws: ϕ ◮ Ex.: p1 ∨ p2 ◮ Executability Laws: ϕ → a ⊤ ◮ Ex.: p2 → a2 ⊤ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 7 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Describing Laws In RAA: 3 types of laws ◮ Static Laws: ϕ ◮ Ex.: p1 ∨ p2 ◮ Executability Laws: ϕ → a ⊤ ◮ Ex.: p2 → a2 ⊤ ◮ Effect Laws: ϕ → [a]ψ ◮ Ex.: p1 → [a1 ]p2 Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 7 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Describing Laws In RAA: 3 types of laws ◮ Static Laws: ϕ ◮ Ex.: p1 ∨ p2 ◮ Executability Laws: ϕ → a ⊤ ◮ Ex.: p2 → a2 ⊤ ◮ Effect Laws: ϕ → [a]ψ ◮ Ex.: p1 → [a1 ]p2 ◮ Frame axioms: ℓ → [a]ℓ ◮ Inexecutability laws: ϕ → [a]⊥ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 7 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Formulas that hold in M a1 p1 , ¬p2 p1 , p2 a2 ◮ p1 ∨ p2 M : a2 a1 ◮ p1 → [a1 ]p2 ◮ p2 → a 2 ⊤ ¬p1 , p2 ◮ ¬p1 → a1 ⊤ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 8 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Formulas that hold in M a1 p1 , ¬p2 p1 , p2 a2 ◮ p1 ∨ p2 M : a2 a1 ◮ p1 → [a1 ]p2 ◮ p2 → a 2 ⊤ ¬p1 , p2 ◮ ¬p1 → a1 ⊤ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 8 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Formulas that hold in M a1 p1 , ¬p2 p1 , p2 a2 ◮ p1 ∨ p2 M : a2 a1 ◮ p1 → [a1 ]p2 ◮ p2 → a 2 ⊤ ¬p1 , p2 ◮ ¬p1 → a1 ⊤ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 8 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Formulas that hold in M a1 p1 , ¬p2 p1 , p2 a2 ◮ p1 ∨ p2 M : a2 a1 ◮ p1 → [a1 ]p2 ◮ p2 → a 2 ⊤ ¬p1 , p2 ◮ ¬p1 → a1 ⊤ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 8 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Formulas that hold in M a1 p1 , ¬p2 p1 , p2 a2 ◮ p1 ∨ p2 M : a2 a1 ◮ p1 → [a1 ]p2 ◮ p2 → a 2 ⊤ ¬p1 , p2 ◮ ¬p1 → a1 ⊤ ± Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 8 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic In our example ◮ Static Law: ◮ coffee → hot ◮ Executability Law: ◮ token → buy ⊤ ◮ Effect Law: ◮ ¬coffee → [buy]coffee ◮ Inexecutability Law: ◮ ¬token → [buy]⊥ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 9 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic In our example ◮ Static Law: ◮ coffee → hot ◮ Executability Law: ◮ token → buy ⊤ ◮ Effect Law: ◮ ¬coffee → [buy]coffee ◮ Inexecutability Law: ◮ ¬token → [buy]⊥ Action Theory T = S ∪ E ∪ X Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 9 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic In our example ◮ Static Law: ◮ coffee → hot ◮ Executability Law: ◮ token → buy ⊤ ◮ Effect Law: ◮ ¬coffee → [buy]coffee ◮ Inexecutability Law: ◮ ¬token → [buy]⊥ Action Theory T = S ∪ E ∪ X What about the Frame, Ramification and Qualification Problems? ◮ No particular solution to the frame problem ◮ Assume we have all relevant frame axioms ◮ Qualification problem: motivation for revision Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 9 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic In our example   coffee → hot, token → buy ⊤,   T =S ∪E ∪X = ¬coffee → [buy]coffee, ¬token → [buy]⊥, coffee → [buy]coffee, hot → [buy]hot   Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 10 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic In our example   coffee → hot, token → buy ⊤,   T =S ∪E ∪X = ¬coffee → [buy]coffee, ¬token → [buy]⊥, coffee → [buy]coffee, hot → [buy]hot   k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, t, ¬c, ¬h Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 10 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Supra-Models Definition M = W , R is a big frame of T iff ◮ W = val(S ) ◮ R = a∈Act R a , where M M R a = {(w , w ′ ) : ∀.ϕ → [a]ψ ∈ Ea , if |= ϕ then |= ′ ψ} w w Definition M M is a supra-model of T iff |= T and M is a big frame of T. Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 11 / 25
    • Preliminaries Action Theories in Multimodal Logic Action Theories in Multimodal Logic Supra-Models   coffee → hot, token → buy ⊤,   T =S ∪E ∪X = ¬coffee → [buy]coffee, ¬token → [buy]⊥, coffee → [buy]coffee, hot → [buy]hot   ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 12 / 25
    • Revision of Laws Semantics of Revision Outline Preliminaries Action Theories in Multimodal Logic Revision of Laws Semantics of Revision Algorithms Conclusion Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 13 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by a law ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make the law true in the model Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by hot → coffee ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make hot ∧ ¬coffee unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by hot → coffee ¬k, ¬t, c, h k, ¬t, c, h b b k, t, c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make hot ∧ ¬coffee unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by hot → coffee ¬k, ¬t, c, h k, ¬t, c, h b b k, t, c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h Make hot ∧ ¬coffee unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by a law ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make the law true in the model Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by token → [buy]¬token ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make token ∧ buy token unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by token → [buy]¬token ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make token ∧ buy token unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by token → [buy]¬token ¬k, ¬t, c, h k, ¬t, c, h b b k, t, c, h k, t, ¬c, h b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make token ∧ buy token unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by a law ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make the law true in the model Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by ¬token → buy ⊤ ¬k, ¬t, c, h k, ¬t, c, h b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make ¬token ∧ [buy]⊥ unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by ¬token → buy ⊤ ¬k, ¬t, c, h k, ¬t, c, h b b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make ¬token ∧ [buy]⊥ unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Intuitions About Model Revision Revision by ¬token → buy ⊤ b b ¬k, ¬t, c, h k, ¬t, c, h b b b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Make ¬token ∧ [buy]⊥ unsatisfiable Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 14 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models ◮ Distance between models ◮ Prefer models closest to the original one ◮ Hamming/Dalal distance, etc Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 15 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models ◮ Distance between models ◮ Prefer models closest to the original one ◮ Hamming/Dalal distance, etc ◮ Distance dependent on the type of law to make valid ◮ Static law: look at the set of possible states (worlds) ◮ Action laws: look at the set of arrows Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 15 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models ◮ Distance between models ◮ Prefer models closest to the original one ◮ Hamming/Dalal distance, etc ◮ Distance dependent on the type of law to make valid ◮ Static law: look at the set of possible states (worlds) ◮ Action laws: look at the set of arrows Definition Let M = W , R . M ′ = W ′ , R ′ is as close to M as M ′′ = W ′′ , R ′′ iff ◮ either W −W ′ ⊆ W −W ′′ ˙ ˙ ◮ or W −W = W −W ′′ and R −R ′ ⊆ R −R ′′ ˙ ′ ˙ ˙ ˙ Notation: M ′ M M ′′ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 15 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by ϕ Definition Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ iff: ⋆ ◮ W ′ = (W val(¬ϕ)) ∪ val(ϕ) ◮ R′ ⊆ R Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 16 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by ϕ Definition Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ iff: ⋆ ◮ W ′ = (W val(¬ϕ)) ∪ val(ϕ) ◮ R′ ⊆ R Definition revise(M , ϕ) = ⋆ min{Mϕ , M} Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 16 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by hot → coffee ¬k, ¬t, c, h k, ¬t, c, h ¬k, ¬t, c, h k, ¬t, c, h ¬k, t, c, h b b b k, t, c, h b k, t, c, h M b b b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, ¬h k, t, ¬c, ¬h Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 17 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by ϕ → [a]ψ Definition Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→[a]ψ iff: ⋆ ◮ W′ = W ◮ R′ ⊆ R M ◮ If (w , w ′ ) ∈ R R ′ , then |= ϕ w M′ ◮ |= ϕ → [a]ψ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 18 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by ϕ → [a]ψ Definition Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→[a]ψ iff: ⋆ ◮ W′ = W ◮ R′ ⊆ R M ◮ If (w , w ′ ) ∈ R R ′ , then |= ϕ w M′ ◮ |= ϕ → [a]ψ Definition revise(M , ϕ → [a]ψ) = ⋆ min{Mϕ→[a]ψ , M} Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 18 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by token → [buy]¬token ¬k, ¬t, c, h k, ¬t, c, h ¬k, ¬t, c, h k, ¬t, c, h b b k, t, c, h k, t, ¬c, h k, t, c, h k, t, ¬c, h M b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 19 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by ϕ → a ⊤ Definition Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→ ⋆ a ⊤ iff: ◮ W′ = W ◮ R ⊆ R′ ◮ If (w , w ′ ) ∈ R ′ R , then w ′ ∈ RelTarget(w , ¬(ϕ → [a]⊥)) M′ ◮ |= ϕ → a ⊤ RelTarget(.): induces effect laws from the models Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 20 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by ϕ → a ⊤ Definition Let M = W , R . M ′ = W ′ , R ′ ∈ Mϕ→ ⋆ a ⊤ iff: ◮ W′ = W ◮ R ⊆ R′ ◮ If (w , w ′ ) ∈ R ′ R , then w ′ ∈ RelTarget(w , ¬(ϕ → [a]⊥)) M′ ◮ |= ϕ → a ⊤ RelTarget(.): induces effect laws from the models Definition revise(M , ϕ → a ⊤) = ⋆ min{Mϕ→ a ⊤, M} Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 20 / 25
    • Revision of Laws Semantics of Revision Minimal Change Choosing models: revising by ¬token → buy ⊤ ◮ coffee: effect of buy, hot: consequence of coffee ◮ token, ¬kitchen: not consequences of coffee b b ¬k, ¬t, c, h k, ¬t, c, h b b b b b b k, t, c, h k, t, ¬c, h b b k, ¬t, ¬c, ¬h k, t, ¬c, ¬h k, ¬t, ¬c, h Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 21 / 25
    • Revision of Laws Algorithms Outline Preliminaries Action Theories in Multimodal Logic Revision of Laws Semantics of Revision Algorithms Conclusion Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 22 / 25
    • Revision of Laws Algorithms Quick look: Revision Algorithms ◮ We have defined algorithms that revise T by Φ, giving T ′ Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 23 / 25
    • Revision of Laws Algorithms Quick look: Revision Algorithms ◮ We have defined algorithms that revise T by Φ, giving T ′ Theorem If T has supra-models, the algorithms are correct w.r.t. our semantics Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 23 / 25
    • Revision of Laws Algorithms Quick look: Revision Algorithms ◮ We have defined algorithms that revise T by Φ, giving T ′ Theorem If T has supra-models, the algorithms are correct w.r.t. our semantics Theorem (Herzig & Varzinczak, AI Journal 2007) We can always ensure T has supra-models Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 23 / 25
    • Revision of Laws Algorithms Quick look: Revision Algorithms ◮ We have defined algorithms that revise T by Φ, giving T ′ Theorem If T has supra-models, the algorithms are correct w.r.t. our semantics Theorem (Herzig & Varzinczak, AI Journal 2007) We can always ensure T has supra-models Theorem Size of T ′ is linear in that of T Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 23 / 25
    • Conclusion Conclusion Contribution ◮ Semantics for action theory revision ◮ Distance between models ◮ Minimal change Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 24 / 25
    • Conclusion Conclusion Contribution ◮ Semantics for action theory revision ◮ Distance between models ◮ Minimal change ◮ Extension of previous work on action theory contraction ◮ Invalidating formulas in a model (KR’2008) Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 24 / 25
    • Conclusion Conclusion Contribution ◮ Semantics for action theory revision ◮ Distance between models ◮ Minimal change ◮ Extension of previous work on action theory contraction ◮ Invalidating formulas in a model (KR’2008) ◮ Syntactic operators (algorithms) ◮ Correct w.r.t. the semantics Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 24 / 25
    • Conclusion Conclusion Ongoing research and future work ◮ Postulates for action theory revision Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 25 / 25
    • Conclusion Conclusion Ongoing research and future work ◮ Postulates for action theory revision ◮ More ‘orthodox’ approach to nonclassical revision Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 25 / 25
    • Conclusion Conclusion Ongoing research and future work ◮ Postulates for action theory revision ◮ More ‘orthodox’ approach to nonclassical revision ◮ Revision of general formulas ◮ not only ϕ, ϕ → a ⊤, ϕ → [a]ψ ◮ more expressive logics: PDL ◮ less expressive logics: Causal Theories of Action Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 25 / 25
    • Conclusion Conclusion Ongoing research and future work ◮ Postulates for action theory revision ◮ More ‘orthodox’ approach to nonclassical revision ◮ Revision of general formulas ◮ not only ϕ, ϕ → a ⊤, ϕ → [a]ψ ◮ more expressive logics: PDL ◮ less expressive logics: Causal Theories of Action ◮ Applications in Description Logics ◮ ontology evolution/debugging Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 25 / 25