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: α ∧ β → ¬ γ Erik Grampp 3(10)

EDAN70 Short recap of logics Propositional logic: α ∧ β → ¬ γ First order / Predicate logic: ∀ x : p ( x ) → q ( x ) Erik Grampp 3(10)

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)

EDAN70 Active logic Labelled formulae Erik Grampp 4(10)

EDAN70 Active logic Labelled formulae Rules of inference Erik Grampp 4(10)

EDAN70 Active logic Labelled formulae Rules of inference label premises ���� � �� � i : α, α → β i + 1 : β � �� � ���� label conclusion Erik Grampp 4(10)

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)

EDAN70 Uses for active logic Reasoning within time Reasoning about time Controlling expansion Erik Grampp 6(10)

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)

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)

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)

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)

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)

EDAN70 The Theorem Prover Developed by Victor Nilsson in 2010 Written in Prolog Erik Grampp 8(10)

EDAN70 My work Modularizing rules Erik Grampp 9(10)

EDAN70 My work Modularizing rules Extending theorem prover Erik Grampp 9(10)

EDAN70 My work Modularizing rules Extending theorem prover Extending belief structure Erik Grampp 9(10)

EDAN70 My work Modularizing rules Extending theorem prover Extending belief structure Creating rules for multiple knowledge bases Erik Grampp 9(10)

EDAN70 My work Modularizing rules Extending theorem prover Extending belief structure Creating rules for multiple knowledge bases K i α A , K i α A → B K i + 1 α B Erik Grampp 9(10)

EDAN70 Questions? Erik Grampp 10(10)