# Logics for Data and Knowledge Representation by ewghwehws

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```									   Logics for Data and Knowledge
Representation
Fausto Giunchiglia

Originally by Alessandro Agostini and Fausto Giunchiglia
Modified by Fausto Giunchiglia and Rui Zhang
Staff                    Contents

Scheduling               Lectures

Reception times          Handouts & Slides

Objective and Outcomes   Other resources

Outline: Introduction

(Abstractio
n)Modeling            Representatio
n            Language
The                  Model
World                                            Theory
Realization           Interpretation

Data
&
Knowledge
A Running example: a picture

 The   world?

A   model?

A   theory?
The world
 The world is everything around us.
 One can only describe a part of the world with certain
degree of abstraction and approximation.
Model
 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
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
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.
Data in the Example
 English:
“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)
…
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.
…”
Behind         Yellow         Right
 Java:
Class Person(String name, String          Light
Right         Pink
Benedeta,red);                          Pink
…
 FOL:
 Diagram:
x,y Person(x)Person(y) Play(x,y)
The picture on the above right.
…
The ER diagram on the right.
Data vs. Knowledge in Different Aspects
Data                    Knowledge
 A factual output of    Statement a class is
physical device         related to another
 Bare facts             Organized facts
 Isolated facts         Related facts
 Direct facts           Processed facts
…                      …

Observed                Axioms + theorems (via
inference/deduction/reas
oning)
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.
Example of Syntax and Semantics
 Supposewe 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)
Levels of Formalization
Both Syntax and Semantics can be formal or
informal.

Diagrams
Programming
NLs         Languages Logics
Level1                        Leveln
English     ER         SQL      PL
Italian   UML          ...    FOL
Russian     ...                DL
Hindi                         ...
...

14
Logics
 What   is a logic for?
Syntax (Webster): the
 Specification
way in which linguistic
 Automation                                      elements (as words) are
put together to form
 Why    logic?                                    constituents (as phrases
   Advantages of a logical framework:                   or clauses)

 Precise Syntax
 Precise Semantics
 Reasoning mechanisms
Semantics (Webster): the
 Which    logic?                         meaning or relationship of
meanings of a sign or set of
   Expressiveness ↔ Complexity          signs especially connotative
meaning
 How    to represent?
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;     off
 satisfactory and economical to use.

   How to measure it?
   time and space consumption
What we refer to in this course

Languages                        Level of Formalization

   Natural Language                Informal
   English, Italian, etc.
   Diagrams                        Semi-formal
   ER, UML, etc.
   Logic                           Formal
   First Order Logic
   Modal Logic
   Description Logics                Focus of the course:
   …                                  How to use logics
What is the message?

Data

Knowledge

Language

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

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