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EDAN70
Active Logic
Erik Grampp
May 22, 2017
Erik Grampp 1(10)
EDAN70
Active logic
Integer labelled logic Introduced by Elgot-Drapkin and Perlis
Erik Grampp 2(10)
Active Logic Erik Grampp May 22, 2017 Erik Grampp 1(10) EDAN70 - - PowerPoint PPT Presentation
Active Logic Erik Grampp May 22, 2017 Erik Grampp 1(10) EDAN70 - - PowerPoint PPT Presentation
EDAN70 Active Logic Erik Grampp May 22, 2017 Erik Grampp 1(10) EDAN70 Active logic Integer labelled logic Introduced by Elgot-Drapkin and Perlis Erik Grampp 2(10) EDAN70 Short recap of logics Propositional logic:
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SLIDE 3
EDAN70
Short recap of logics
Propositional logic: α ∧ β → ¬γ
Erik Grampp 3(10)
SLIDE 4
EDAN70
Short recap of logics
Propositional logic: α ∧ β → ¬γ First order / Predicate logic: ∀x : p(x) → q(x)
Erik Grampp 3(10)
SLIDE 5
EDAN70
Short recap of logics
Propositional logic: α ∧ β → ¬γ First order / Predicate logic: ∀x : p(x) → q(x) Modal logic: α ∧ ♦β → ♦γ
Erik Grampp 3(10)
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EDAN70
Active logic
Labelled formulae
Erik Grampp 4(10)
SLIDE 7
EDAN70
Active logic
Labelled formulae Rules of inference
Erik Grampp 4(10)
SLIDE 8
EDAN70
Active logic
Labelled formulae Rules of inference
label
- i :
premises
- α, α → β
i + 1 :
label
β
- conclusion
Erik Grampp 4(10)
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EDAN70
Active logic
Basic rules of inference: i : . . . i + 1 : Now(i + 1) i : A, A → B i + 1 : B i : A i + 1 : A
Erik Grampp 5(10)
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EDAN70
Uses for active logic
Reasoning within time Reasoning about time Controlling expansion
Erik Grampp 6(10)
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EDAN70
Reasoning about time
The Three Wise Men Problem All three can see each others hats At least one blue hat
Erik Grampp 7(10)
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EDAN70
Reasoning about time
The Three Wise Men Problem All three can see each others hats At least one blue hat Solution:
Erik Grampp 7(10)
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EDAN70
Reasoning about time
The Three Wise Men Problem All three can see each others hats At least one blue hat Solution: No two white hats: the one who saw them would know
Erik Grampp 7(10)
SLIDE 14
EDAN70
Reasoning about time
The Three Wise Men Problem All three can see each others hats At least one blue hat Solution: No two white hats: the one who saw them would know No one white hat: the one who saw it would know
Erik Grampp 7(10)
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EDAN70
Reasoning about time
The Three Wise Men Problem All three can see each others hats At least one blue hat Solution: No two white hats: the one who saw them would know No one white hat: the one who saw it would know Therefore: three blue hats
Erik Grampp 7(10)
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EDAN70
The Theorem Prover
Developed by Victor Nilsson in 2010 Written in Prolog
Erik Grampp 8(10)
SLIDE 17
EDAN70
My work
Modularizing rules
Erik Grampp 9(10)
SLIDE 18
EDAN70
My work
Modularizing rules Extending theorem prover
Erik Grampp 9(10)
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EDAN70
My work
Modularizing rules Extending theorem prover Extending belief structure
Erik Grampp 9(10)
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EDAN70
My work
Modularizing rules Extending theorem prover Extending belief structure Creating rules for multiple knowledge bases
Erik Grampp 9(10)
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EDAN70
My work
Modularizing rules Extending theorem prover Extending belief structure Creating rules for multiple knowledge bases Ki
αA, Ki αA → B
Ki+1
α B
Erik Grampp 9(10)
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EDAN70
Questions?
Erik Grampp 10(10)