1. Logics for Data and Knowledge Representation
Fausto Giunchiglia
Originally by Alessandro Agostini and Fausto Giunchiglia
Modified by Fausto Giunchiglia and Rui Zhang

2. Forehead Staff Contents Scheduling Lectures Reception times
Course website
Objective and Outcomes
Prerequisites
Contents
Lectures
Handouts & Slides
Readings
Other resources
Exam policy & Grading

3. Outline: Introduction
(Abstraction)Modeling
Representation
Model
Language
Theory
The World
Realization
Interpretation
Data
&
Knowledge

4. What are we talking about?
A Running example: a picture
The world?
A model?
A theory?

5. The world The world is everything around us.
One can only describe a part of the world with certain degree of abstraction and approximation.

6. Example: a model of the world from the picture
An abstraction of a part of the world.
Domain: the set of objects that are interested.
Individual: single item in the domain.
Set: group of individuals sharing common properties
Relation: set of pairs of individuals
Example: a model of the world from the picture

7. Example: a model of the world from the picture
Language
English
Natural Language: Italian, Chinese, …
Java
Programming Language: C, Python, …
Picture
Diagram: photo, ER, UML, …
FOL
Logic: Modal Logic, DLs, …
Example: a model of the world from the picture

8. Theory Theory = Data + Knowledge (about the model)
Data: A collection of facts from which conclusions may be drawn.
Useful irrelevant or redundant facts, which must be processed to be meaningful.
Used as a basis for reasoning, discussion or calculation (Merriam-Webster).
Knowledge: How to use a language to represent and structure the facts. The sum of what is known.
Knowledge is data in context, or organized data, or also data in relationship.

9. Data in the Example English: Java: Diagram: FOL: Person(Benedeta)
“There are 3 girls playing in the snow…”
Java:
P1 = new Person(Benedeta,red); …
Diagram:
the pictures on the right.
FOL:
Person(Benedeta)
ClothColor(Benedata,Red)

10. Knowledge in the Example
English:
“The figure with head, arms, body, legs represents a person. The white stuff represents snow. The grew stuffs are mountains. …”
Java:
Class Person(String name, String Benedeta,red); …
Diagram:
The picture on the above right.
The ER diagram on the right.
Behind
Yellow
Right
Light Pink
Right
Pink
FOL:
x,y Person(x)Person(y) Play(x,y) …

11. Data vs. Knowledge in Different Aspects
A factual output of physical device
Bare facts
Isolated facts
Direct facts …
Observed
Knowledge
Statement a class is related to another
Organized facts
Related facts
Processed facts …
Axioms + theorems (via inference/deduction/reas oning)
Bare vs. Organized: some pixels vs. pixels form images of persons
Isolated vs. Related: pixel(200,300) is RGB(254,0,0) vs. pixel(200,300) to pixel(300,500) are white snow
Direct vs. Processed(by human/ pattern recognition): raw vs. reasoning/inference

12. Syntax and Semantics Syntax: the way a language is written.
Syntax is determined by a set of “rules” saying how to construct the expressions of the language from the set of atomic tokens (i.e., terms, characters, symbols).
The set of atomic token is called alphabet of symbols, or simply the alphabet).
Semantics: the way a language is interpreted.
determines the meaning of syntactic constructs (expressions), that is, the relationship between syntactic constructs and the elements of some universe of meanings (the model).
such relationship is called interpretation.

13. Example of Syntax and Semantics
Suppose we want to represent the fact that Benedetta and Eleonora are near each other.
By using English we may write (syntax): Benedetta is near to Eleonora.
By using a ‘symbolized’ English we may write (syntax): near(B,E), or extensively near(Benedetta,Eleonora)
To fix the semantics of “near(B,E)” we need to fix an interpretation I of it, i.e., “near” by I means near (spatial relation) “B” by I means Benedetta (a girl) “E” by I means Eleonora (a girl)

14. Levels of Formalization
Both Syntax and Semantics can be formal or informal.
Diagrams
Programming Languages
NLs
Logics
Level1
Leveln
English Italian Russian Hindi ...
ER UML ...
SQL ...
PL FOL DL ... 14

15. Logics What is a logic for? Why logic? Which logic? How to represent?
Specification
Automation
Why logic?
Advantages of a logical framework:
Precise Syntax
Precise Semantics
Reasoning mechanisms
Which logic?
Expressiveness ↔ Complexity
How to represent?
Syntax (Webster): the way in which linguistic elements (as words) are put together to form constituents (as phrases or clauses)
Semantics (Webster): the meaning or relationship of meanings of a sign or set of signs especially connotative meaning

16. Efficiency VS. Effectiveness
Task of the modeler: an appropriate representation
Effectiveness (with language: expressiveness)
What is it?
Adequate to accomplish a purpose;
producing the intended result.
How to measure it?
completeness and correctness
Efficiency (with a language: complexity)
Performing in the best possible manner;
satisfactory and economical to use.
time and space consumption
Trade-off

17. What we refer to in this course
Languages
Level of Formalization
Natural Language
English, Italian, etc.
Diagrams
ER, UML, etc.
Logic
First Order Logic
Modal Logic
Description Logics …
Informal
Semi-formal
Formal
Focus of the course:
How to use logics

18. What is the message?
Expressions
Language
Knowledge
Data

19. Exercises What is in the comic? What is the data?
What is the knowledge?
Represent the comic in English(natural Language)
List at least 3 schemas to represent the comic and try to formalize the contents with them.