Presentation on theme: "Zoran Majkic Integration of Ontological Bayesian Logic Programs"— Presentation transcript:
1 Zoran Majkic Integration of Ontological Bayesian Logic Programs in Deductive Knowledge SystemsZoran MajkicComputer Science Dept.University of MarylandCollege ParkSeptember 2005
2 Motivation: Biological Ontologies Data Bases and OntologiesInformation retrieval from unstructured Biomedical dataGenome databases and AnnotationRepresentation of sequence data and functional infoBiological Data IntegrationBiological Data warehouseExperimental facts and aggregationsBiological DataminingRelational datamining
3 Motivation: Semantic Web for Genomics Major chalenge for post genomic eraFormal Ontologies: provide consensus representation of bioinformatics dataMulti agent systems – modular middleware: Web servicesAdvanced relational data mining: generate probabilistic knowledgeAutomated access to specific units of information
4 From Bayesian Networks to Relational Databases Bayesian ClauseA A1 ,…. An[Majkic 2004, 2005]Ontological Bayesian ProgramsA A1 ,…. AnRelational Data base
5 Bayesian Network: Genetics and Probability Has a probabilistic nature given by the biological laws of inheritanceRequires the representation of the relational familiar structure of the objects under studyBayesian Network:A qualitative component – acyclic influence graph among the random variablesA quantitative component that ecodes Probability density over these local influences
6 Example: Individual’s phenotype “each individual ha a polygenic value, or polygenotape, which in the population is normally (Gaussian density) distributed”“each gene independently effects additive changes of the phenotype” (ex. height of a person)Values of phenotype when the number of underlying genes increases:
7 Example: Probability Density apriory density175Aposteriory density(m + f) / 2 = 168.5
8 Example: Dependency graph f = 173Inheritance of height :(m+f)/2 = 168.5m = 164
9 Bayesian Clause: A A1 ,….., An Atoms: A = p(t1,…, t_k), with Dom(p) different from true values = (true, false).Ground atoms = random variables in Bayesian networkSymbol: complex probability distribution operation is not logic implicationExample: “blood-type bt of a person X depends on the inherited information of X”Each person X has two copies of the chromosome containing gene, mc(Y), pc(Z), inherited from her mother m(Y,X) and father f(Z,X) :bt(X) mc(X, pc(X)With Dom(bt) = a, b, ab, 0 , Dom(mc) = Dom(pc) = a, b, 0 .
10 Bayesian Clause: probabilistic model Conditional probability distribution of a clause cBayesian program:m(ann, dorothy) , f(brian, dorothy), pc(ann), pc(brian), mc(brian), mc(ann)mc(X) m(Y,X) , mc(Y) , pc(Y)pc(X) f(Y,X) , mc(Y) , pc(Y)bt(X) mc(X) , pc(X)
11 Herbrand models ? Logic: Herbrand model I: H 2 , 2 = (true, false). Example: I(m(ann, dorothy)) = true, I(m(dorothy, ann))= falseProblem: Bayesian model I: H W , W is not 2.Example: I(mc(ann)) in W = a, b, , or higher types,I(bt(dorothy)) in W = F(x,y) : x,y in a,b,0Solution: Higher-order Herbrand model type Iabs: H W, with Iabs(A): W 2, and for any w in W,Iabs (A)(w) = true if and only if I(A) = w
12 Program transformation: flattening Higher-order Herbrand interpretationA type T denotes a functional spaceHidden parametersTransformation of AtomsFlattened interpretation withfor anyExample : for
13 Example: FlatteningHigher-order Herbrand model type Iabs: H T, whereT = ( 2 W2 )W1 with W1 =Dom(bt) = a, b, ab, 0 , W2 = [0,1].m(ann, dorothy) ……………… bt(dorothy)= …………… ( 2 W2 )W1Transformation: bt(X) btF(X, w1, w2)
14 Ontological Bayesian Program Two-valued logic programUnique Herbrand model IF : HFExample:for the case whenwe obtain
15 Advantages: full integration More expressive Bayesian environment:We can use negation:We can use constraints:Full integration with Relational Databases and Deductive Databases: Standard Query LanguageCommon Ontology DB
16 ReferencesZ. Majkic, Ontological encapsulation of many-valued logic, 19th Italian Symposium of Computational Logic (CILC04), June 16-17, Parma, Italy, 2004Z.Majkic, Constraint Logic Programming and Logic Modality for Event's Valid-time Approximation, 2nd Indian International Conference on Artificial Intelligence (IICAI-05), December 20-22, 2005, Pune, India.Z.Majkic, Beyond Fuzzy: Parameterized approximations of Heyting algebras for uncertain knowledge, 2nd Indian International Conference on Artificial Intelligence (IICAI-05), December 20-22, 2005, Pune, India.Z. Majkic, Kripke Semantics for Higher-order Herbrand Model Types, Technical Report, 2005 , College Park, University of Maryland.
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