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On the Revision of Action Laws: an Algorithmic Approach

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Ivan Varzinczak

This document discusses revising the laws that govern the behavior of actions in action theories. It presents an algorithmic approach to revising action laws based on observations that contradict the existing knowledge base. The document is presented at the NRAC'2009 conference and is divided into sections on preliminaries regarding action theories in multimodal logic, the semantics and algorithms for revising action laws, and a conclusion.

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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

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On the Revision of Action Laws: an Algorithmic Approach

  • 1. 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
  • 2. Motivation Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 2 / 25
  • 3. 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
  • 4. 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
  • 5. 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
  • 6. 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
  • 7. 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
  • 8. 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
  • 9. 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
  • 10. 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
  • 11. 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
  • 12. 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
  • 13. Outline Preliminaries Action Theories in Multimodal Logic Ivan Jos´ Varzinczak (KSG - Meraka) e On the Revision of Action Laws NRAC’2009 3 / 25
  • 14. 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
  • 15. 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
  • 16. 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
  • 17. 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
  • 18. 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
  • 19. 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
  • 20. 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
  • 21. 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
  • 22. 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
  • 23. 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
  • 24. 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
  • 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
  • 26. 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
  • 27. 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
  • 28. 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
  • 29. 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
  • 30. 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
  • 31. 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
  • 32. 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
  • 33. 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
  • 34. 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
  • 35. 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
  • 36. 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
  • 37. 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
  • 38. 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
  • 39. 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
  • 40. 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
  • 41. 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
  • 42. 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
  • 43. 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
  • 44. 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
  • 45. 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
  • 46. 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
  • 47. 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
  • 48. 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
  • 49. 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
  • 50. 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
  • 51. 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
  • 52. 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
  • 53. 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
  • 54. 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
  • 55. 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
  • 56. 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
  • 57. 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
  • 58. 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
  • 59. 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
  • 60. 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
  • 61. 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
  • 62. 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
  • 63. 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
  • 64. 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
  • 65. 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
  • 66. 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
  • 67. 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
  • 68. 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
  • 69. 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
  • 70. 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
  • 71. 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
  • 72. 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
  • 73. 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
  • 74. 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
  • 75. 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