The Father Guido Sarducci Slide
-
Upload
ila-reeves -
Category
Documents
-
view
17 -
download
0
description
Transcript of The Father Guido Sarducci Slide
1
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
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) …
Title Author Language
Book42 Moby Dick Melville English
Books43 Lao Tzy Lao Tzu Chinese
Book44 Ramayana Valmiki Sanskrit
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”