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FiRE Fuzzy Reasoning Engine

FiRE Fuzzy Reasoning Engine. Nikolaos Simou National Technical University of Athens. Outline. Introduction to f- SHIN Syntax Semantics Fuzzy Reasoning Engine FiRE Syntax Reasoning Services FiRE Integration with Sesame Benefits Demonstration. Uncertainty and knowledge representation.

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FiRE Fuzzy Reasoning Engine

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  1. FiREFuzzy Reasoning Engine Nikolaos Simou National Technical University of Athens

  2. Outline • Introduction to f-SHIN • Syntax • Semantics • Fuzzy Reasoning Engine FiRE • Syntax • Reasoning Services • FiRE Integration with Sesame • Benefits • Demonstration

  3. Uncertainty and knowledge representation • Uncertainty is part of our lives… i.e. tall, fat, soon • Description Logics (DLs) lacks the ability to represent imprecise or vague information • This representation is necessary for many application domains (medical informatics, multimedia processing) • DLs were extended using fuzzy set theory

  4. Fuzzy Set Theory • An object belongs to a fuzzy set to any degree between 0 and 1. • Tall(Tom) = 0.7 • Set theoretic operations are performed by mathematical functions • 1-xis used for negation • min(x,y)for intersection • max(x,y) for union • max(1-x,y) for implications

  5. SHIN • SHIN is an AL language • AL-language is represented by a string of the form AL[U][E][N][C] U: union E: full existential quantification N:Number Restrictions C:Complement (negation) • Negation is like union and full existential quantification • ALC = ALUE • Similar for roles S : transitive roles H : role implication I : inverse roles

  6. Syntax of Fuzzy SHIN • f-SHIN concepts are formed in the same way as in SHIN C,D ::=⊤ | ⊥ | ¬C | C⊓ D | C⊔ D |∃R.C | ∀R.C| ≥nR | ≤nR R,P::= R- | Trans(R) | P⊑R

  7. Fuzzy knowledge bases • A fuzzy knowledge base is a triple Σ= (T ,R, A) where: • T is a finite set of fuzzy inclusion axioms: A ⊑ C or fuzzyequivalences: A≡C, called a fuzzy TBox • R is a finite set of fuzzy transitive role axioms: Trans(R) orfuzzy role inclusion axioms P ⊑ R, called a fuzzy RBox • A is a finite set of fuzzy assertions: 〈 a : C⋈ n 〉 or〈 (a, b) : R⋈n 〉, where ⋈ ∈ {≥,>,<, ≤}, called a fuzzy ABox.

  8. Semantics of f-SHIN • A fuzzy interpretation is a pair I= (ΔI× .I) where ΔIis the domain of interpretation and .I is the interpretation function which maps • An individual name α∈ I to an element α I∈ ΔI • A concept name A to a membership function AI: ΔI→[0,1] • A role name R to a membership function RI: ΔI× ΔI→[0,1]

  9. Extending semantics to complex concepts

  10. Interpreting Axioms

  11. FiRE • FiRE is a Fuzzy Reasoning Engine implemented using JAVA • Currently supports f-SHIN DL Language • Consist of an alphabet of concepts (C) roles (R) and individuals (I)

  12. Declaring Alphabet • Alphabet declaration is made using the keyword signature and it is divided into three smaller declarations the concepts declaration using keyword atomic-concepts, the roles declaration using keyword roles and the individualsdeclaration using keyword individuals.

  13. Declaring Alphabet -An Example (signature :atomic-concepts (human person female male woman man parentC mother father sister brother parent-having-many-children tall clever thin organised parent-NOT-having-many-children parent-having-3-children beautifull fast strong) :roles ((has-gender :transitive t) (has-descendant :transitive t) (has-child :inverse has-descendant) (has-sibling) (has-degree) (has-sister) (has-brother) ( has-friend) ) :individuals (Alice Betty Charles Doris Eve Peter))

  14. Declaring Alphabet • Roles are declared using keyword roles. Each role is defined within brackets and it may have one or more of the following parameters

  15. f-SHIN Constructors Syntax

  16. Declaring Axioms • There are two kinds of axioms inclusion and equivalence. • Defined concept has to be an atomic concept and on the other hand property concept can be an atomic concept or a result of f-SHIN constructors. • Syntax • (implies/equivalent definedConc propertyConc) • Examples • (implies man (and person (some has-gender male))) • (equivalent father-having-only-sons (and man (all has-child man)))

  17. Declaring Assertions • Fuzzy Instances • Syntax Using the keyword instance followed by the individual, the concept the inequality symbol (>,>=,<,<=) and the degree of participation. • Example (instanceCharles brother) (instanceCharles (and tall thin) >= 0.7 )

  18. Declaring Assertions • Fuzzy Relations • Syntax Using the keyword related followed by the individuals names, the role that relates them, the inequality type and the degree of participation • Examples (related Peter Betty has-sister ) (related Peter Charles has-friend >= 0.8 )

  19. FiRE Interface The FiRE user interface consists of an editor pane (upper left), inference services pane (upper right-Entailment, Subsumption,Glb), and output pane (the bottom-Tableaux Expansion, Output, Tableaux, Model, Classification).

  20. Reasoning Services • Consistency • Checks the knowledge for consistency. • The Tableaux expansion pane presents the tableaux expansion in detail showing all the operators applied. • The Output pane shows the statements declared, or differently the syntax mistakes • The Tableaux pane shows the results of tableaux expansion • The model pane shows the resulting model.

  21. Reasoning Services • Entailment • Entailment queriesevaluatewhetheranindividual participatesin a concept with a specific degree. FiRE answers true or false to these queries • Syntax (instanceindividualconcept ⋈ degree) or individual concept ⋈ degree • Example ( instance Doris (and human (some has-gender (or female male))) >= 1) or Doris (and human (some has-gender (or female male))) >= 1

  22. Reasoning Services • Subsumption • Subsumption queries evaluate whether a concept is subsumed by another concept. FiRE answers true or false to these queries • Syntax (implies C1 C2) or C1 C2 • Example ( implies father man) or father man • Greatest Lower Bound • Greatestlowerboundqueries evaluate the greatest possible degree of an individual participatingin a concept • Syntax Similar to entailment queries

  23. Reasoning Services • Classification This action performs subsumption checks of all the possible combinations of concepts and it creates the taxonomy tree shown in Classification Pane.

  24. What is sesame • Sesame is an open source Java framework • Storing • Querying and • Reasoning with RDF and RDF Schema. (also supports N3, N-Triple, Turtle) • It can be used • As a database for RDF and RDF Schema • As a Java library for applications that need to work with RDF internally

  25. Sesame Architecture

  26. Sesame Integration • Converts knowledge to N-Triples and exports it to Sesame • Evaluates greatest lower bound for all the individuals participating in all the concepts (Global GLB) and exports implicit knowledge to Sesame. • Imports knowledge from sesame and evaluates Global GLB

  27. Benefits • Data Stored in a sesame repository • Data can then easily stored to a database • Server-Client Architecture • Easy access to data • Queries • Which individual is tall > 0.6, clever > 0.5 and also has a sister? • Reasoning is off-line operation

  28. Future Extensions • Apply DL Optimizations. • Fuzzy Queries • Extend to other uncertainty formalisms. • Extend the DL component’s expressiveness (SHOIN exist). • Support data types. • Support rules.

  29. FiRE URL • You can download FiRE from http://www.image.ece.ntua.gr/~nsimou/

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