1. Karen Wickett School of Information University of Texas at Austin
INF385T: Information Modeling The Father Guido Sarducci Slides and some final comments Slides for November 30, 2016
Karen Wickett School of Information University of Texas at Austin

2. The Father Guido Sarducci IM 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 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 at the A-box or instance level:
“text42 realizes Moby Dick”

13. Grammars and Graphs We use grammars to define modeling languages
We can use graphs to understand the results of our modeling
Parse trees are a kind of graph that lets us trace the generation of an expression and confirm that it is in our language
We can also use graphs to make assertions
a la the RDF graph language
but then we still need to serialize the graph in order to use it computationally.