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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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