1 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

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. {,, …} Or, alternatively, as a conjunction of dyadic predications… Titled(book42, “Moby Dick”) & Authored(book42, Melville) & hasLanguage(book42,English) … TitleAuthorLanguage Book42Moby DickMelvilleEnglish Books43Lao TzyLao TzuChinese Book44RamayanaValmikiSanskrit

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”