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The Father Guido Sarducci Slide

LIS590IM Information Modeling — Slide Set for Class 16 The Father Guido Sarducci Slide and some final comments Slides for Dec 16 lecture. LIS590IML: Information Modeling Allen Renear Graduate School of Library and Information Science University of Illinois, Urbana-Champaign Fall 2008.

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The Father Guido Sarducci Slide

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  1. LIS590IM Information Modeling — Slide Set for Class 16The Father Guido SarducciSlideand some final commentsSlides for Dec 16 lecture LIS590IML: Information ModelingAllen RenearGraduate School of Library and Information ScienceUniversity of Illinois, Urbana-Champaign Fall 2008

  2. The Father Guido Sarducci Slide • Expressiveness (vs efficiency, decidability, completeness) • Data independence

  3. Logic Logic is the foundation for all information modeling, past and future. Sometimes the connection is implicit (RDMSs), sometimes explicit. You understand a modeling system if, and only if, you understand the logic it is based on. Parts of a logical system • Syntax • Teller’s formation rules • Semantics • Teller’s evaluation rules (including “interpretations” • Inferencing systems • Truth tables • Truth trees • Natural deduction

  4. Expressiveness Information modeling languages vary in their expressiveness…. • Predication • none (sentences only) • monadic • polyadic • Quantification over individual variables • Selection of truth functional connectives • Quantification over predicate variables • Modal notions (necessity, probability) • Epistemic notions (belief, knowledge, justification)

  5. Expressiveness vs Algorithmic • Some inferencing techniques are algorithms some aren’t. • truth tables and truth trees are algorithms • ND is not • Some logics have an algorithmic inferencing techniques, some don’t. • SL has many algorithmic techniques • PL has none (though truth trees is an algorithm most of the time)

  6. Expressiveness vs. Efficiency • Some inferencing algorithms are efficient in some circumstances some aren’t • truth tables are catastrophically inefficient for full SL • very efficient for RDF • truth trees are very efficient, except when the aren’t • As certain kinds of expressiveness goes up efficiency can go down • reasoning over the EC fragment of FOL (I.e. RDF) is always very efficient • reasoning over SL can, in the worst case, be very inefficient

  7. Expressiveness vs. Decidability • Sometime increases in expressiveness can make a system undecidable • In full FOL there is no algorithm that will derive every valid conclusion

  8. Database tables • Tables are relations, sets of n-tuples. • that why we say “relational database”

  9. A Table [EN]

  10. A Relation { < >, < >, < >, < >, < } >,

  11. Relations, triples, predications The information carried by a relation with n-sized tuples can be re-expressed by a relation of 3-sized tuples, i.e. triples. { <book42, title, “Moby Dick”>, < book42, Author, Melville>, < book42, Language, English> …} Or, alternatively, as a conjunction of dyadic predications… Titled(book42, “Moby Dick”) & Authored(book42, Melville) & hasLanguage(book42,English) …

  12. Conceptual Models, such as ER diagrams • A conceptual model is a representation of the possibilities and a constraints for a domain. • They can be translated into FOL axioms • They function at the T-Box or schema level, representing the possibilities and contraints • “if x is a an expression then there exists a y such that y realizes y and y is a work” • Not a the A-box or instance level: • “text42 realizes Moby Dick”

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