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FOIL v 6.4

This document provides a comprehensive overview of the FOIL v6.4 system, detailing the Domain Model and Knowledge Base components. It breaks down various predicates, rules, and concepts within the FOIL framework, illustrating how member relationships and components interact. The content covers strategies for selecting literals and evaluating coverage, emphasizing the importance of determining gainful literals in rule generation. Additionally, the roadmap offers insight into available packages and utilities that enhance the functionality of the FOIL system.

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FOIL v 6.4

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  1. FOIL v6.4 P. Jiménez

  2. RoadMap • Foil v.6.4 • DomainModel

  3. RoadMap • Foil v.6.4 • DomainModel

  4. KNOWLEDGE BASE components([1],1,[]). components([2],2,[]). components([13],1,[3]). components([21],2,[1]). components([22],2,[2]). components([112],1,[12]). components([231],2,[31]). components([313],3,[13]). … member(1,[1]). member(3,[3]). member(1,[11]). member(1,[13]). member(1,[31]). member(3,[33]). member(3,[113]). member(1,[131]). … not(member(1,[])). not(member(1,[3])). not(member(1,[33])). not(member(1,[333])). … ¿Member(X0,X1)?

  5. CONCEPTS • Target Literal • member(X0, X1) • Rule • member(X0, X1) :- components(X1, X0, X2) • RuleSet • member(X0, X1) :- components(X1, X0, X2) • member(X0, X1) :- • components(X1, X2, X3), member(X0, X3)

  6. CONCEPTS • Predicates • member, components • PredicateTypes • Target: member • Support: components • Predefined: equal • Arguments and Arity • Member/2 [element, list] • Components/3 [list, element, list] • Equal/2

  7. CONCEPTS • Literals • member(X0,X1) • Predicatemember/2 [element, list] • Argumentlist (Terms) <X0, X1> • Signnotnegated • !equal(X0,C0) • Predicateequal[element, element] • Argumentlist (Terms) <X0, C0> • Signnegated

  8. Concepts ¿Member(X0,X1)? Bindings <X0 = 1, X1 = [131]> <X0 = 3, X1 = [131]> <X0 = 1, X1 = [133]> <X0 = 3, X1 = [133]> <X0 = 1, X1 = [311]> <X0 = 3, X1 = [311]> <X0 = 1, X1 = [313]> <X0 = 3, X1 = [313]> <X0 = 1, X1 = [331]> <X0 = 3, X1 = [331]> <X0 = 3, X1 = [333]> <X0 = 1, X1 = [1]> <X0 = 3, X1 = [3]> <X0 = 1, X1 = [11]> <X0 = 1, X1 = [13]> <X0 = 1, X1 = [13]> <X0 = 3, X1 = [13]> <X0 = 3, X1 = [31]> <X0 = 3, X1 = [33]> <X0 = 1, X1 = [111]> <X0 = 1, X1 = [113]> <X0 = 3, X1 = [113]> Coverage

  9. GeneratingCandidates Member(X0, X1) X1=“[1]” X0 = “1” components(X1,New0,New1) … … Member(X0, X2) … !X0=“1” !X1=“[1]” !components(X1,New0,New1) … … ! Member(X0, X2) … Vi = C Vi = Vj Q(V1, V2, …, Vk) !Vi = c !Vi = Vj !Q(V1, V2, …, Vk)

  10. EvaluatingCoverage Candidate Literal X0 = “1” <X0 = 1, X1 = [1]> <X0 = 3, X1 = [3]> <X0 = 1, X1 = [11]> <X0 = 1, X1 = [13]> <X0 = 1, X1 = [13]> <X0 = 3, X1 = [13]> <X0 = 3, X1 = [31]> <X0 = 3, X1 = [33]> <X0 = 1, X1 = [111]> <X0 = 1, X1 = [113]> <X0 = 3, X1 = [113]> <X0 = 1, X1 = [131]> <X0 = 3, X1 = [131]> <X0 = 1, X1 = [133]> <X0 = 3, X1 = [133]> <X0 = 1, X1 = [311]> <X0 = 3, X1 = [311]> <X0 = 1, X1 = [313]> <X0 = 3, X1 = [313]> <X0 = 1, X1 = [331]> <X0 = 3, X1 = [331]> <X0 = 3, X1 = [333]> Coverage Data 11 15

  11. EvaluatingCoverage components(X1,New0,New1) <X0 = 1, X1 = [1]> <X0 = 3, X1 = [3]> <X0 = 1, X1 = [11]> <X0 = 1, X1 = [13]> <X0 = 1, X1 = [1], X2 = 1, X3 = []> components([1],1,[]). <X0 = 3, X1 = [3] , X2 = 3, X3 = []> components([3],3,[]). components([11],1,[1]). <X0 = 1, X1 = [11] , X2 = 1, X3 = [11]> … member(X0,New0) <X0 = 1, X1 = [1]> <X0 = 1, X1 = [1] , X2 = [1]> <X0 = 1, X1 = [1] , X2 = [11]> <X0 = 1, X1 = [1] , X2 = [13]> member(1,[1]). member(1,[11]). member(1,[13]).

  12. Type of Literals • Determinate literal • Introduces new variables • The new parcial rule has exactlyonetupleforeach positive tuple in thecurrent rule and at mostonetupleforeachnegativetuple • Gainful literal • Mayincreasetheproportion of positive tuples • May introduce new variables

  13. SelectingLiterals • The literal withgreatestgain (80% UsefulGain) • Alldeterminateliteralsfound • The literal withhighest positive gain • A literal that introduces a new variable

  14. RoadMap • Foil v.6.4 • DomainModel

  15. DomainModel • SeePackage Data • SeePackageDataCoverage • SeePackegeKnowledgeBase and KnowledgeBaseFactory

  16. Branch & Bound

  17. DomainModel • SeepackageHeuristic • SeePackageLiteralFactory • SeePackageAnalyst • SeepackageUtilities

  18. DomainModel • SeePackageBranch & Bound

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