Re: Monotonic abduction and Bayes theorem in N3 coherent logic

The results in http://eulersharp.sourceforge.net/2007/07test/wetE100.n3
and http://eulersharp.sourceforge.net/2007/07test/wetE101.n3
are actually containing e:inductivity triples according to
http://eulersharp.sourceforge.net/2003/03swap/log-rules.n3

e:inductivity a rdf:Property;
                 rdfs:comment """a property to express the ratio 
possibleModels/(possibleModels+counterModels)""";
                 rdfs:domain rdfs:Resource;
                 rdfs:range xsd:decimal .

which is like closing the monotonic abduction-deduction-induction cycle 
aka "monadic".

Kind regards,

Jos De Roo | Agfa HealthCare
Senior Researcher | HE/Advanced Clinical Applications Research
T  +32 3444 7618
http://www.agfa.com/w3c/jdroo/

Agfa HealthCare NV, Moutstraat 100, 9000 Gent, Belgium
http://www.agfa.com/healthcare




Jos De Roo/AMDUS/AGFA 
09/14/2010 11:34 PM

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Subject
Monotonic abduction and Bayes theorem in N3 coherent logic






http://eulersharp.sourceforge.net/2007/07test/wetP100.n3
contains 100 historical measurements for location 1 plus some integrity 
constraints

http://eulersharp.sourceforge.net/2007/07test/wetC100.n3
contains the actual condition for location 1

http://eulersharp.sourceforge.net/2007/07test/wetQ100.n3
http://eulersharp.sourceforge.net/2007/07test/wetQ101.n3
are 2 questions 

The thesis is that for query Q given condition C
belief(Q|C) = possibleModels/(possibleModels+counterModels)

i.e. for http://eulersharp.sourceforge.net/2007/07test/wetE100.n3
belief(Sprinkler|WetGrass) = 46/(46+35) = 0.56790

and for http://eulersharp.sourceforge.net/2007/07test/wetE101.n3
belief(Rain|WetGrass) = 54/(54+27) = 0.66667

With appropriate queries and conditions the Bayes theorem holds:
belief(Sprinkler|WetGrass) = 
belief(WetGrass|Sprinkler)*belief(Sprinkler)/belief(WetGrass)
        46/(46+35) = 46/(46+5)*51/(51+49)/(81/(81+19)) = 0.56790
belief(Rain|WetGrass) = 
belief(WetGrass|Rain)*belief(Rain)/belief(WetGrass)
        54/(54+27) = 54/(54+4)*58/(58+42)/(81/(81+19)) = 0.66667


Jos De Roo | Agfa HealthCare
Senior Researcher | HE/Advanced Clinical Applications Research
T  +32 3444 7618
http://www.agfa.com/w3c/jdroo/

Agfa HealthCare NV, Moutstraat 100, 9000 Gent, Belgium
http://www.agfa.com/healthcare