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
1
The Father Guido Sarducci Slide
• Expressiveness (vs efficiency, decidability, completeness)
• Data independence
2
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
3
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)
4
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)
5
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
6
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
7
Database tables
• Tables are relations, sets of n-tuples.
•
that why we say “relational database”
8
A Table [EN]
9
A Relation
{<
<
<
<
<
>,
>,
>,
>,
>, }
10
Relations, triples, predications
Title
Author
Language
Book42
Moby Dick
Melville
English
Books43
Lao Tzy
Lao Tzu
Chinese
Book44
Ramayana
Valmiki
Sanskrit
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) …
11
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”
12