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LIS590IM Information Modeling — Slide Set for Class 16

The Father Guido SarducciSlide

and some final comments

Slides for Dec 16 lecture

LIS590IML: Information ModelingAllen Renear

Graduate School of Library and Information ScienceUniversity of Illinois, Urbana-Champaign

Fall 2008

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The Father Guido Sarducci Slide

• Expressiveness (vs efficiency, decidability, completeness)

• Data independence

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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

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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)

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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)

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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

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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

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Database tables

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

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A Table [EN]

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A Relation

{

}

<<<<<

>,>,>,>,>,

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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) …

Title Author Language

Book42 Moby Dick Melville English

Books43 Lao Tzy Lao Tzu Chinese

Book44 Ramayana Valmiki Sanskrit

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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”