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 Course website Objective and Outcomes Prerequisites Contents Lectures Handouts & Slides Readings Other resources Exam policy & Grading

Outline: Introduction (Abstraction)Modeling Representation Model Language Theory The World 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.

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

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: 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)

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) …

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

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 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)

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

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

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

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

What is the message? Expressions Language Knowledge Data

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.