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Chapter X: On the Relation between AA, ABA and LP Martin Caminada - - PowerPoint PPT Presentation
Chapter X: On the Relation between AA, ABA and LP Martin Caminada - - PowerPoint PPT Presentation
Chapter X: On the Relation between AA, ABA and LP Martin Caminada Department of Computing Science University of Aberdeen Overview ABA LP AA Overview ABA LP AA Overview ABA LP stable preferred grounded complete ideal AA Overview
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Overview
ABA LP AA
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Overview
ABA LP AA
stable preferred grounded complete ideal
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Overview
ABA LP AA
stable preferred grounded complete ideal semi-stable
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Overview
ABA LP AA
stable preferred grounded complete ideal semi-stable
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Overview
ABA LP AA
stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable
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Overview
ABA LP AA
stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable
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Overview
ABA LP AA
stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable
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Overview
ABA LP AA
stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable
DeLP
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Overview
ABA LP AA
stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable stable preferred grounded complete ideal semi-stable
DeLP
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Translating ABA to LP
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Translating ABA to LP
starting point: an ABA framework that is flat, unique-contrary and non-assumption contrary
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Translating ABA to LP
starting point: an ABA framework that is flat, unique-contrary and non-assumption contrary idea:
- each ABA rule becomes an LP rule
- replace each assumption α by not α
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Translating ABA to LP
starting point: an ABA framework that is flat, unique-contrary and non-assumption contrary idea:
- each ABA rule becomes an LP rule
- replace each assumption α by not α
Example:
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Translating ABA to LP
starting point: an ABA framework that is flat, unique-contrary and non-assumption contrary idea:
- each ABA rule becomes an LP rule
- replace each assumption α by not α
Example: a ← b, c, δ, ε
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Translating ABA to LP
starting point: an ABA framework that is flat, unique-contrary and non-assumption contrary idea:
- each ABA rule becomes an LP rule
- replace each assumption α by not α
Example: a ← b, c, δ, ε a ← b, c, not d, not e (assuming δ = d and ε = e)
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From LP model to ABA labelling
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From LP model to ABA labelling
starting point: (3-valued) model <T,F> of PF
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From LP model to ABA labelling
starting point: (3-valued) model <T,F> of PF α with α ∈ F becomes in α with α ∈ T becomes out α with α ∈ HBPF \ (T U F) becomes undec
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From LP model to ABA labelling
starting point: (3-valued) model <T,F> of PF α with α ∈ F becomes in (just like α with α Ï HBPF ) α with α ∈ T becomes out α with α ∈ HBPF \ (T U F) becomes undec
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From LP model to ABA labelling
starting point: (3-valued) model <T,F> of PF α with α ∈ F becomes in (just like α with α Ï HBPF ) α with α ∈ T becomes out α with α ∈ HBPF \ (T U F) becomes undec LP model assumption labelling 3-valued stable complete 2-valued stable stable regular preferred well-founded grounded ideal ideal
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From ABA labelling to LP model
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From ABA labelling to LP model
starting point: assumption labelling of ABA framework F
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From ABA labelling to LP model
starting point: assumption labelling of ABA framework F T': each α ∈ HBPF where α is out F': each α ∈ HBPF where α is in
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From ABA labelling to LP model
starting point: assumption labelling of ABA framework F T': each α ∈ HBPF where α is out F': each α ∈ HBPF where α is in <T, F> = Φ(PF
<T',F'>)
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From ABA labelling to LP model
starting point: assumption labelling of ABA framework F T': each α ∈ HBPF where α is out F': each α ∈ HBPF where α is in <T, F> = Φ(PF
<T',F'>)
assumption labelling LP model complete 3-valued stable stable 2-valued stable preferred regular grounded well-founded ideal ideal
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Translating LP to ABA
P → FP → PFP
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Translating LP to ABA
P → FP → PFP = P
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Translating LP to ABA
P → FP → PFP = P LP model assumption labelling 3-valued stable complete 2-valued stable stable regular preferred well-founded grounded ideal ideal
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Translating LP to ABA
P → FP → PFP = P assumption labelling LP model complete 3-valued stable stable 2-valued stable preferred regular grounded well-founded ideal ideal
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Take Home Message
ABA = LP and LP = ABA ABA writes α, β, γ instead of not a, not b, not c ABA semantics are defined
- nly on the weakly negated part of the program;