L ogics for D ata and K nowledge R epresentation

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

2. Forehead • Staff • Scheduling • 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. 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

7. 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: “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. • FOL: x,y Person(x)Person(y) Play(x,y) … Behind Yellow Right Light Pink Right Pink

11. Data vs. Knowledge in Different Aspects Data • 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/reasoning)

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 ofsyntacticconstructs (expressions), that is, the relationship between syntacticconstructs 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 extensivelynear(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 ProgrammingLanguages NLs Logics Level1 Leveln PLFOLDL... EnglishItalianRussianHindi... SQL... ERUML... 14

15. Logics • What is a logic for? • 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) • What is it? • Performing in the best possible manner; • satisfactory and economical to use. • How to measure it? • 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.