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
 Forehead
Staff                    Contents

Scheduling               Lectures

Reception times          Handouts & Slides

Course website           Readings

Objective and Outcomes   Other resources

Prerequisites            Exam policy & Grading
Outline: Introduction


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


                                                   Data
                                                    &
                                                 Knowledge
What are we talking about?
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)
     What is it?                                 Trade-
       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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