Logics for Data and Knowledge Representation Fausto Giunchiglia

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

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

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

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

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

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

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

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

Data in the Example q English: “There are 3 girls playing in the snow…” q Java: P 1 = new Person(Benedeta, red); … q Diagram: the pictures on the right. q FOL: Person(Benedeta) Cloth. Color(Benedata, Red) …

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

Data vs. Knowledge in Different Aspects Data q A factual output of physical device q Bare facts q Isolated facts q Direct facts q… Knowledge q Statement a class is related to another q Organized facts q Related facts q Processed facts q… Observed Axioms + theorems (via inference/deduction/re asoning)

Syntax and Semantics q Syntax: the way a language is written. q 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). q The set of atomic token is called alphabet of symbols, or simply the alphabet). q Semantics: the way a language is interpreted. q determines the meaning of syntactic constructs (expressions), that is, the relationship between syntactic constructs and the elements of some universe of meanings (the model). q such relationship is called interpretation.

Example of Syntax and Semantics q Suppose we want to represent the fact that Benedetta and Eleonora are near each other. q By using English we may write (syntax): Benedetta is near to Eleonora. q By using a ‘symbolized’ English we may write (syntax): near(B, E), or extensively near(Benedetta, Eleonora) q 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 Level 1 English Italian Russian Hindi. . . SQL. . . ER UML. . . 14 Leveln PL FOL DL. . .

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

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

What we refer to in this course Languages Natural Language Informal Semi-formal Formal ER, UML, etc. Logic English, Italian, etc. Diagrams Level of Formalization 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. 2. 3. 4. 5. 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.