# Artificial Intelligence

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Artificial Intelligence ICS461 Fall Lecture #12B More Representations Outline Logics Rules Frames Nancy E. Reed 2 Representation Agents deal with knowledge (data) Facts (believe & observe knowledge) Procedures (how to knowledge) Meaning g( (relate & define knowledge) Right representation is critical to success Early realisation of importance in AI Wrong choice can lead to project failure Still an active research area Choosing a Representation For certain problem solving techniques Best representation already known Often a requirement of the technique Or a requirement of the programming language (e.g. Prolog) Examples First order theorem proving first order logic Inductive logic programming logic programs Neural networks learning neural networks Some general representation schemes Suitable for many different (and new) AI applications Some General Representations Logical Representations Production Rules Conceptual graphs, frames Description and Multivalued Logics What is a Logic? A language with concrete rules No ambiguity in representation (may be other errors!) Allows unambiguous communication and processing Very unlike natural languages e.g. English Many ways to translate between languages A statement can be represented in different logics And perhaps differently in same logic Expressiveness of a logic How much can we say in this language? Not to be confused with logical reasoning Logics are languages, reasoning is a process (may use logic) 1

2 Logic is a Good Representation Fairly easy to do the translation when possible Branches of mathematics devoted to it It enables us to do logical reasoning Tools and techniques come for free Basis for programming languages Prolog uses logic programs (a subset of FOL) λprolog based on HOL Syntax and Semantics Syntax Rules for constructing legal sentences in the logic Which symbols we can use (English: letters, punctuation) How we are allowed to combine symbols Semantics How we interpret (read) sentences in the logic Assigns a meaning to each sentence Example: All lecturers are seven feet tall A valid sentence (syntax) And we can understand the meaning (semantics) This sentence happens to be false (there is a counterexample) The idea is that knowledge is often best understood as a set of concepts that are related to one another. The meaning of a concept is defined by its relationship to other concepts. A semantic network consists of 1. a set of nodes that are 2. connected by labeled arcs. The nodes represent concepts and the arcs represent relations between concepts. Common Semantic Relations There is no standard set of relations for semantic networks, but the following relations are very common: INSTANCE: X is an INSTANCE of Y if X is a specific example of the general concept Y. Example: Elvis is an INSTANCE of Human ISA: X ISA Y if X is a subset of the more general concept Y. Example: sparrow ISA bird HASPART: X HASPART Y if the concept Y is a part of the concept X. (Or this can be any other property) Example: sparrow HASPART tail Inheritance Inheritance is a key concept in semantic networks and can be represented naturally by following ISA links. In general, if concept X has property P, then all concepts that are a subset of X should also have property P. But exceptions are pervasive in the real world! In practice, inherited properties are usually treated as default values. If a node has a direct link that contradicts an inherited property, then the default is overridden. 2

3 Multiple Inheritance Multiple inheritance allows an object to inherit properties from multiple concepts. Multiple inheritance can sometimes allow an object to inherit conflicting properties. Conflicts are potentially unavoidable, so conflict resolution strategies are needed. Representing Events Jack kidnapped Billy on August 5 Kidnapping Event Kidnap1 perpetrator: Jack victim: Billy date: August 5 Representing Predicates Representing Relations score(bows, Otherguys, 34-8 Karl John Game Instance: Game17 hometeam: Bows Visiting team: Otherguys Score: 34-8 height Height1 greater-than height2 height Non-Logical Representations? Production rules Semantic networks Conceptual graphs Frames Logic representations have restrictions and can be hard to work with Many AI researchers searched for better representations Production Rules Rule set of <condition,action> pairs if condition then action Match-resolve-act cycle Match: Agent checks if each rule s condition holds Resolve: - Multiple production rules may fire at once (conflict set) - Agent must choose rule from set (conflict resolution) Act: If so, rule fires and the action is carried out Working memory: rule can write knowledge to working memory knowledge may match and fire other rules 3

4 Graphical Representations People draw diagrams all the time, e.g. Causal relationships Graphical Representation Graphs easy to store in a computer To be of any use must impose a formalism And relationships between ideas Jason is 15, Bryan is 40, Arthur is 70, Jim is 74 How old is Julia? Because the syntax is the same We can guess that Julia s age is similar to Bryan s Formalism imposes restricted syntax Graphical representation Links indicate subset, member, relation,... Equivalent to logical statements (usually FOL) Easier to understand than FOL? Specialised SN reasoning algorithms can be faster Example: natural language understanding Sentences with same meaning have same graphs e.g. Conceptual Dependency Theory (Schank) Conceptual Graphs Semantic network where each graph represents a single proposition Concept nodes can be Concrete (visualisable) such as restaurant, my dog Spot Abstract (not easily visualisable) such as anger Edges do not have labels l Instead, conceptual relation nodes Easy to represent relations between multiple objects Frames A frame represents an entity as a set of slots (attributes) and associated values. Each slot may have constraints that describe legal values that the slot can take. A frame can represent a specific entity, or a general concept. Frames are implicitly associated with one another because the value of a slot can be another frame. 4

5 Frame Representations Example: Frame Representation Semantic networks where nodes have structure Frame with a number of slots (age, height,...) Each slot stores specific item of information When agent faces a new situation Slots can be filled in (value may be another frame) Filling in may trigger actions May trigger retrieval of other frames Inheritance of properties between frames Very similar to objects in OOP Flexibility in Frames Slots in a frame can contain Information for choosing a frame in a situation Relationships between this and other frames Procedures to carry out after various slots filled Default information to use where input is missing i Blank slots: left blank unless required for a task Other frames, which gives a hierarchy Can also be expressed in first order logic Demons One of the main advantages of frames is the ability to include demons to compute slot values. Demon - a function that computes the value of a slot on demand. HUMAN isa: (MAMMAL) mortal: (yes :inheritable yes) cardinality: (6 million :inheritable no) age: (:inheritable yes :demon compute_age) MARY instance: HUMAN gender: FEMALE birthday: 11/04/60 int Compute_Age (frame) return(today- (query birthday slot)); Features of Frame Representations Frames can support values more naturally than semantic nets (e.g. the value 25) Frames can be easily implemented using object-oriented programming techniques. Demons allow for arbitrary functions to be embedded in a representation. But a price is paid in terms of efficiency, generality, and modularity! Inheritance can be easily controlled. Comparative Issues in Knowledge Representation The semantics behind a knowledge representation model depends on the way that it is used (implemented). Notation is irrelevant! Whether a statement is written in logic or as a semantic network is not important -- what matters is whether the knowledge is used in the same manner. Most knowledge representation models can be made to be functionally equivalent. It is a useful exercise to try converting knowledge in one form to another form. From a practical perspective, the most important consideration usually is whether the KR model allows the knowledge to be encoded and manipulated in a natural fashion. 5

6 Expressiveness of Semantic Nets Some types of properties are not easily expressed using a semantic network. For example: negation, disjunction, and general non-taxonomic knowledge. There are specialized ways of dealing with these relationships, for example partitioned semantic networks and procedural attachment. But these approaches are ugly and not commonly used. Negation can be handled by having complementary predicates (e.g., A and NOT A) and using specialized procedures to check for them. Also very ugly, but easy to do. If the lack of expressiveness is acceptable, semantic nets have several advantages: inheritance is natural and modular, and semantic nets can be quite efficient. Representation & Logic Some wanted non-logical representations Production rules Semantic networks - Conceptual graphs, frames Bt But all can be expressed din first order logic! i! Best of both worlds Logical reading ensures representation well-defined Representations specialised for applications Can make reasoning easier, more intuitive Inheritance Comparison Semantic networks and frames are often used because inheritance is represented so naturally. But rule based systems can also do inheritance Semantic networks (and frames) have an implementation advantage for inheritance because special-purpose algorithms can be used to follow the ISA links. Representation Comparisons Rules are appropriate for some types of knowledge, but do not easily map to others. Semantic nets can easily represent inheritance and exceptions, but are not well-suited for representing negation, disjunction, preferences, conditionals, and cause/effect relationships. Frames allow arbitrary functions (demons) and typed inheritance. Implementation is a bit more cumbersome. Summary Knowledge Representations Logic Rules Frames 6

### Foundations of Artificial Intelligence. Knowledge Representation and Reasoning

Foundations of Artificial Intelligence Knowledge Representation and Reasoning Knowledge Based Systems The field of knowledge engineering can be defined as the process of assessing problems, acquiring knowledge

### Lecture 5: Introduction to Knowledge Representation

Lecture 5: Introduction to Knowledge Representation Dr. Roman V Belavkin BIS4410 Contents 1 Knowledge Engineering Knowledge Engineering Definition 1 (Knowledge Engineering). The process of designing knowledgebased

### FUNDAMENTALS OF ARTIFICIAL INTELLIGENCE KNOWLEDGE REPRESENTATION AND NETWORKED SCHEMES

Riga Technical University Faculty of Computer Science and Information Technology Department of Systems Theory and Design FUNDAMENTALS OF ARTIFICIAL INTELLIGENCE Lecture 7 KNOWLEDGE REPRESENTATION AND NETWORKED

### Predicate logic Proofs Artificial intelligence. Predicate logic. SET07106 Mathematics for Software Engineering

Predicate logic SET07106 Mathematics for Software Engineering School of Computing Edinburgh Napier University Module Leader: Uta Priss 2010 Copyright Edinburgh Napier University Predicate logic Slide 1/24

### Introduction to knowledge representation and reasoning. We now look briefly at how knowledge about the world might be represented and reasoned with.

Introduction to knowledge representation and reasoning We now look briefly at how knowledge about the world might be represented and reasoned with. Aims: To introduce semantic networks and frames for knowledge

### SEARCHING AND KNOWLEDGE REPRESENTATION. Angel Garrido

Acta Universitatis Apulensis ISSN: 1582-5329 No. 30/2012 pp. 147-152 SEARCHING AND KNOWLEDGE REPRESENTATION Angel Garrido ABSTRACT. The procedures of searching of solutions of problems, in Artificial Intelligence

### IAI : Knowledge Representation

IAI : Knowledge Representation John A. Bullinaria, 2005 1. What is Knowledge? 2. What is a Knowledge Representation? 3. Requirements of a Knowledge Representation 4. Practical Aspects of Good Representations

### æ A collection of interrelated and persistent data èusually referred to as the database èdbèè.

CMPT-354-Han-95.3 Lecture Notes September 10, 1995 Chapter 1 Introduction 1.0 Database Management Systems 1. A database management system èdbmsè, or simply a database system èdbsè, consists of æ A collection

### Logic in general. Inference rules and theorem proving

Logical Agents Knowledge-based agents Logic in general Propositional logic Inference rules and theorem proving First order logic Knowledge-based agents Inference engine Knowledge base Domain-independent

### CSL105: Discrete Mathematical Structures. Ragesh Jaiswal, CSE, IIT Delhi

Propositional Logic: logical operators Negation ( ) Conjunction ( ) Disjunction ( ). Exclusive or ( ) Conditional statement ( ) Bi-conditional statement ( ): Let p and q be propositions. The biconditional

### ! " # The Logic of Descriptions. Logics for Data and Knowledge Representation. Terminology. Overview. Three Basic Features. Some History on DLs

,!0((,.+#\$),%\$(-&.& *,2(-\$)%&2.'3&%!&, Logics for Data and Knowledge Representation Alessandro Agostini agostini@dit.unitn.it University of Trento Fausto Giunchiglia fausto@dit.unitn.it The Logic of Descriptions!\$%&'()*\$#)

### Fundamental Computer Science Concepts Sequence TCSU CSCI SEQ A

Fundamental Computer Science Concepts Sequence TCSU CSCI SEQ A A. Description Introduction to the discipline of computer science; covers the material traditionally found in courses that introduce problem

Computing and Informatics, Vol. 20, 2001,????, V 2006-Nov-6 UPDATES OF LOGIC PROGRAMS Ján Šefránek Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics, Comenius University,

### A terminology model approach for defining and managing statistical metadata

A terminology model approach for defining and managing statistical metadata Comments to : R. Karge (49) 30-6576 2791 mail reinhard.karge@run-software.com Content 1 Introduction... 4 2 Knowledge presentation...

### COMPUTER SCIENCE TRIPOS

CST.98.5.1 COMPUTER SCIENCE TRIPOS Part IB Wednesday 3 June 1998 1.30 to 4.30 Paper 5 Answer five questions. No more than two questions from any one section are to be answered. Submit the answers in five

### 060010706- Artificial Intelligence 2014

Module-1 Introduction Short Answer Questions: 1. Define the term Artificial Intelligence (AI). 2. List the two general approaches used by AI researchers. 3. State the basic objective of bottom-up approach

### Artificial Intelligence. Knowledge Representation

RC Chakraborty 03/03 to 08/3, 2007, Lecture 15 to 22 (8 hrs) Slides 1 to 79 myreaders, http://myreaders.wordpress.com/, rcchak@gmail.com (Revised Feb. 02, 2008) Artificial Intelligence Knowledge Representation

### Reusable Knowledge-based Components for Building Software. Applications: A Knowledge Modelling Approach

Reusable Knowledge-based Components for Building Software Applications: A Knowledge Modelling Approach Martin Molina, Jose L. Sierra, Jose Cuena Department of Artificial Intelligence, Technical University

### The Foundations: Logic and Proofs. Chapter 1, Part III: Proofs

The Foundations: Logic and Proofs Chapter 1, Part III: Proofs Rules of Inference Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build Arguments

### The Language of Mathematics

CHPTER 2 The Language of Mathematics 2.1. Set Theory 2.1.1. Sets. set is a collection of objects, called elements of the set. set can be represented by listing its elements between braces: = {1, 2, 3,

### Software Engineering. System Models. Based on Software Engineering, 7 th Edition by Ian Sommerville

Software Engineering System Models Based on Software Engineering, 7 th Edition by Ian Sommerville Objectives To explain why the context of a system should be modeled as part of the RE process To describe

### Course Syllabus For Operations Management. Management Information Systems

For Operations Management and Management Information Systems Department School Year First Year First Year First Year Second year Second year Second year Third year Third year Third year Third year Third

### Mathematics for Computer Science/Software Engineering. Notes for the course MSM1F3 Dr. R. A. Wilson

Mathematics for Computer Science/Software Engineering Notes for the course MSM1F3 Dr. R. A. Wilson October 1996 Chapter 1 Logic Lecture no. 1. We introduce the concept of a proposition, which is a statement

### A set is a Many that allows itself to be thought of as a One. (Georg Cantor)

Chapter 4 Set Theory A set is a Many that allows itself to be thought of as a One. (Georg Cantor) In the previous chapters, we have often encountered sets, for example, prime numbers form a set, domains

### Introduction to Knowledge Fusion and Representation

Introduction to Knowledge Fusion and Representation Introduction 1. A.I. 2. Knowledge Representation 3. Reasoning 4. Logic 5. Information Integration 6. Semantic Web Knowledge Fusion Fall 2004 1 What is

### Classification of Fuzzy Data in Database Management System

Classification of Fuzzy Data in Database Management System Deval Popat, Hema Sharda, and David Taniar 2 School of Electrical and Computer Engineering, RMIT University, Melbourne, Australia Phone: +6 3

### Software Verification and Testing. Lecture Notes: Z I

Software Verification and Testing Lecture Notes: Z I Motivation so far: we have seen that properties of software systems can be specified using first-order logic, set theory and the relational calculus

### CS510 Software Engineering

CS510 Software Engineering Propositional Logic Asst. Prof. Mathias Payer Department of Computer Science Purdue University TA: Scott A. Carr Slides inspired by Xiangyu Zhang http://nebelwelt.net/teaching/15-cs510-se

### COMP 378 Database Systems Notes for Chapter 7 of Database System Concepts Database Design and the Entity-Relationship Model

COMP 378 Database Systems Notes for Chapter 7 of Database System Concepts Database Design and the Entity-Relationship Model The entity-relationship (E-R) model is a a data model in which information stored

### 2. The Language of First-order Logic

2. The Language of First-order Logic KR & R Brachman & Levesque 2005 17 Declarative language Before building system before there can be learning, reasoning, planning, explanation... need to be able to

### Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture - 17 Shannon-Fano-Elias Coding and Introduction to Arithmetic Coding

### Algorithms, Flowcharts & Program Design. ComPro

Algorithms, Flowcharts & Program Design ComPro Definition Algorithm: o sequence of steps to be performed in order to solve a problem by the computer. Flowchart: o graphical or symbolic representation of

### M.Tech. DEGREE EXAMINATION, DEC. - 2013 (Examination at the end of Final Year) Computer Science. Paper - I : ADVANCED DATABASE MANAGEMENT SYSTEMS

(DMTCS 21) M.Tech. DEGREE EXAMINATION, DEC. - 2013 (Examination at the end of Final Year) Computer Science Paper - I : ADVANCED DATABASE MANAGEMENT SYSTEMS Time : 03 Hours Maximum Marks : 75 Answer question

### Introduction. Database Management Systems

Introduction Database Management Systems Database Management System (DBMS) Collection of interrelated data and set of programs to access the data Convenient and efficient processing of data Database Application

### Generalized Modus Ponens

Generalized Modus Ponens This rule allows us to derive an implication... True p 1 and... p i and... p n p 1... p i-1 and p i+1... p n implies p i implies q implies q allows: a 1 and... a i and... a n implies

### SQL DDL. Applied Databases. Inclusion Constraints. Key Constraints

Applied Databases Handout 2. Database Design. 5 October 2010 SQL DDL In its simplest use, SQL s Data Definition Language (DDL) provides a name and a type for each column of a table. CREATE TABLE Hikers

### Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Add and subtract within 20. MP.

Performance Assessment Task Incredible Equations Grade 2 The task challenges a student to demonstrate understanding of concepts involved in addition and subtraction. A student must be able to understand

### Introduction to Logic in Computer Science: Autumn 2006

Introduction to Logic in Computer Science: Autumn 2006 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 Plan for Today Now that we have a basic understanding

### Computational Logic in an Object-Oriented World

Computational Logic in an Object-Oriented World Robert Kowalski Imperial College London rak@doc.ic.ac.uk Abstract Logic and object-orientation (OO) are competing ways of looking at the world. Both view

### Policy Modeling and Compliance Verification in Enterprise Software Systems: a Survey

Policy Modeling and Compliance Verification in Enterprise Software Systems: a Survey George Chatzikonstantinou, Kostas Kontogiannis National Technical University of Athens September 24, 2012 MESOCA 12,

### WOLLONGONG COLLEGE AUSTRALIA. Diploma in Information Technology

First Name: Family Name: Student Number: Class/Tutorial: WOLLONGONG COLLEGE AUSTRALIA A College of the University of Wollongong Diploma in Information Technology Final Examination Spring Session 2008 WUCT121

### The CLIPS environment. The CLIPS programming language. CLIPS production rules language - facts. Notes

The CLIPS environment The CLIPS environment CLIPS is an environment to develop knowledge based systems It defines a programming language that allows to represent declarative and procedural knowledge This

### Circuits and Boolean Expressions

Circuits and Boolean Expressions Provided by TryEngineering - Lesson Focus Boolean logic is essential to understanding computer architecture. It is also useful in program construction and Artificial Intelligence.

### Lecture 12: Entity Relationship Modelling

Lecture 12: Entity Relationship Modelling The Entity-Relationship Model Entities Relationships Attributes Constraining the instances Cardinalities Identifiers Generalization 2004-5 Steve Easterbrook. This

### [Refer Slide Time: 05:10]

Principles of Programming Languages Prof: S. Arun Kumar Department of Computer Science and Engineering Indian Institute of Technology Delhi Lecture no 7 Lecture Title: Syntactic Classes Welcome to lecture

### COURSE DESCRIPTION FOR THE COMPUTER INFORMATION SYSTEMS CURRICULUM

COURSE DESCRIPTION FOR THE COMPUTER INFORMATION SYSTEMS CURRICULUM Course Code 2505100 Computing Fundamentals Pass/ Fail Prerequisite None This course includes an introduction to the use of the computer

### Information Brokering over the Information Highway: An Internet-Based Database Navigation System

In Proc. of The Joint Pacific Asian Conference on Expert Systems, Singapore, 1997 Information Brokering over the Information Highway: An Internet-Based Database Navigation System Syed Sibte Raza ABIDI

### WHAT ARE MATHEMATICAL PROOFS AND WHY THEY ARE IMPORTANT?

WHAT ARE MATHEMATICAL PROOFS AND WHY THEY ARE IMPORTANT? introduction Many students seem to have trouble with the notion of a mathematical proof. People that come to a course like Math 216, who certainly

### (LMCS, p. 317) V.1. First Order Logic. This is the most powerful, most expressive logic that we will examine.

(LMCS, p. 317) V.1 First Order Logic This is the most powerful, most expressive logic that we will examine. Our version of first-order logic will use the following symbols: variables connectives (,,,,

### Relations: their uses in programming and computational specifications

PEPS Relations, 15 December 2008 1/27 Relations: their uses in programming and computational specifications Dale Miller INRIA - Saclay & LIX, Ecole Polytechnique 1. Logic and computation Outline 2. Comparing

### A Knowledge-based System for Translating FOL Formulas into NL Sentences

A Knowledge-based System for Translating FOL Formulas into NL Sentences Aikaterini Mpagouli, Ioannis Hatzilygeroudis University of Patras, School of Engineering Department of Computer Engineering & Informatics,

### Overview of the TACITUS Project

Overview of the TACITUS Project Jerry R. Hobbs Artificial Intelligence Center SRI International 1 Aims of the Project The specific aim of the TACITUS project is to develop interpretation processes for

### EFFICIENT KNOWLEDGE BASE MANAGEMENT IN DCSP

EFFICIENT KNOWLEDGE BASE MANAGEMENT IN DCSP Hong Jiang Mathematics & Computer Science Department, Benedict College, USA jiangh@benedict.edu ABSTRACT DCSP (Distributed Constraint Satisfaction Problem) has

### Algorithm & Flowchart & Pseudo code. Staff Incharge: S.Sasirekha

Algorithm & Flowchart & Pseudo code Staff Incharge: S.Sasirekha Computer Programming and Languages Computers work on a set of instructions called computer program, which clearly specify the ways to carry

### Updating Action Domain Descriptions

Updating Action Domain Descriptions Thomas Eiter, Esra Erdem, Michael Fink, and Ján Senko Institute of Information Systems, Vienna University of Technology, Vienna, Austria Email: (eiter esra michael jan)@kr.tuwien.ac.at

### Lecture 16 : Relations and Functions DRAFT

CS/Math 240: Introduction to Discrete Mathematics 3/29/2011 Lecture 16 : Relations and Functions Instructor: Dieter van Melkebeek Scribe: Dalibor Zelený DRAFT In Lecture 3, we described a correspondence

### Discuss the size of the instance for the minimum spanning tree problem.

3.1 Algorithm complexity The algorithms A, B are given. The former has complexity O(n 2 ), the latter O(2 n ), where n is the size of the instance. Let n A 0 be the size of the largest instance that can

### SIT102 Introduction to Programming

SIT102 Introduction to Programming After working through this session you should: Understand the relationships between operating systems, their user interfaces, and programs; Understand the difference

### International Journal of Scientific & Engineering Research, Volume 4, Issue 11, November-2013 5 ISSN 2229-5518

International Journal of Scientific & Engineering Research, Volume 4, Issue 11, November-2013 5 INTELLIGENT MULTIDIMENSIONAL DATABASE INTERFACE Mona Gharib Mohamed Reda Zahraa E. Mohamed Faculty of Science,

### TECH. Requirements. Why are requirements important? The Requirements Process REQUIREMENTS ELICITATION AND ANALYSIS. Requirements vs.

CH04 Capturing the Requirements Understanding what the customers and users expect the system to do * The Requirements Process * Types of Requirements * Characteristics of Requirements * How to Express

### University of Ostrava. Reasoning in Description Logic with Semantic Tableau Binary Trees

University of Ostrava Institute for Research and Applications of Fuzzy Modeling Reasoning in Description Logic with Semantic Tableau Binary Trees Alena Lukasová Research report No. 63 2005 Submitted/to

### Announcements. SE 1: Software Requirements Specification and Analysis. Review: Use Case Descriptions

Announcements SE 1: Software Requirements Specification and Analysis Lecture 4: Basic Notations Nancy Day, Davor Svetinović http://www.student.cs.uwaterloo.ca/ cs445/winter2006 uw.cs.cs445 Send your group

### Scheduling Shop Scheduling. Tim Nieberg

Scheduling Shop Scheduling Tim Nieberg Shop models: General Introduction Remark: Consider non preemptive problems with regular objectives Notation Shop Problems: m machines, n jobs 1,..., n operations

### An Object Model for Business Applications

An Object Model for Business Applications By Fred A. Cummins Electronic Data Systems Troy, Michigan cummins@ae.eds.com ## ## This presentation will focus on defining a model for objects--a generalized

### Unit 2.1. Data Analysis 1 - V2.0 1. Data Analysis 1. Dr Gordon Russell, Copyright @ Napier University

Data Analysis 1 Unit 2.1 Data Analysis 1 - V2.0 1 Entity Relationship Modelling Overview Database Analysis Life Cycle Components of an Entity Relationship Diagram What is a relationship? Entities, attributes,

### Relational model. Relational model - practice. Relational Database Definitions 9/27/11. Relational model. Relational Database: Terminology

COS 597A: Principles of Database and Information Systems elational model elational model A formal (mathematical) model to represent objects (data/information), relationships between objects Constraints

### High School Algebra Reasoning with Equations and Inequalities Solve equations and inequalities in one variable.

Performance Assessment Task Quadratic (2009) Grade 9 The task challenges a student to demonstrate an understanding of quadratic functions in various forms. A student must make sense of the meaning of relations

### Cassandra. References:

Cassandra References: Becker, Moritz; Sewell, Peter. Cassandra: Flexible Trust Management, Applied to Electronic Health Records. 2004. Li, Ninghui; Mitchell, John. Datalog with Constraints: A Foundation

### Chapter 1: Key Concepts of Programming and Software Engineering

Chapter 1: Key Concepts of Programming and Software Engineering Software Engineering Coding without a solution design increases debugging time - known fact! A team of programmers for a large software development

### Inconsistency Measurement and Remove from Software Requirement Specification

Inconsistency Measurement and Remove from Software Requirement Specification 1 karuna patel, 2 Prof.Snehal Gandhi 1 Computer Department 1 Sarvajanik College of Engineering and Technology, Surat, Gujarat,

### Predicate Logic. M.A.Galán, TDBA64, VT-03

Predicate Logic 1 Introduction There are certain arguments that seem to be perfectly logical, yet they cannot be specified by using propositional logic. All cats have tails. Tom is a cat. From these two

### VISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University

VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS

### 4.1. Definitions. A set may be viewed as any well defined collection of objects, called elements or members of the set.

Section 4. Set Theory 4.1. Definitions A set may be viewed as any well defined collection of objects, called elements or members of the set. Sets are usually denoted with upper case letters, A, B, X, Y,

### Integrating Cognitive Models Based on Different Computational Methods

Integrating Cognitive Models Based on Different Computational Methods Nicholas L. Cassimatis (cassin@rpi.edu) Rensselaer Polytechnic Institute Department of Cognitive Science 110 8 th Street Troy, NY 12180

### 1 What is Machine Learning?

COS 511: Theoretical Machine Learning Lecturer: Rob Schapire Lecture #1 Scribe: Rob Schapire February 4, 2008 1 What is Machine Learning? Machine learning studies computer algorithms for learning to do

### Database Concepts. Database & Database Management System. Application examples. Application examples

Database & Database Management System Database Concepts Database = A shared collection of logically related (and a description of this data), designed to meet the information needs of an organization.

### CSE 459/598: Logic for Computer Scientists (Spring 2012)

CSE 459/598: Logic for Computer Scientists (Spring 2012) Time and Place: T Th 10:30-11:45 a.m., M1-09 Instructor: Joohyung Lee (joolee@asu.edu) Instructor s Office Hours: T Th 4:30-5:30 p.m. and by appointment

### Big Data Analytics. Rasoul Karimi

Big Data Analytics Rasoul Karimi Information Systems and Machine Learning Lab (ISMLL) Institute of Computer Science University of Hildesheim, Germany Big Data Analytics Big Data Analytics 1 / 1 Introduction

### II. Conceptual Modeling

II. Conceptual Modeling Engineering Software Models in Software Engineering What is Conceptual Modeling? Origins 2003 John Mylopoulos and Steve Easterbrook Conceptual Modeling -- 1 Engineering Software

### Rigorous Software Development CSCI-GA 3033-009

Rigorous Software Development CSCI-GA 3033-009 Instructor: Thomas Wies Spring 2013 Lecture 11 Semantics of Programming Languages Denotational Semantics Meaning of a program is defined as the mathematical

### Lecture 7: NP-Complete Problems

IAS/PCMI Summer Session 2000 Clay Mathematics Undergraduate Program Basic Course on Computational Complexity Lecture 7: NP-Complete Problems David Mix Barrington and Alexis Maciel July 25, 2000 1. Circuit

### Semantic Search in Portals using Ontologies

Semantic Search in Portals using Ontologies Wallace Anacleto Pinheiro Ana Maria de C. Moura Military Institute of Engineering - IME/RJ Department of Computer Engineering - Rio de Janeiro - Brazil [awallace,anamoura]@de9.ime.eb.br

### Static Analysis and Validation of Composite Behaviors in Composable Behavior Technology

Static Analysis and Validation of Composite Behaviors in Composable Behavior Technology Jackie Zheqing Zhang Bill Hopkinson, Ph.D. 12479 Research Parkway Orlando, FL 32826-3248 407-207-0976 jackie.z.zhang@saic.com,

### Predicate Calculus. There are certain arguments that seem to be perfectly logical, yet they cannot be expressed by using propositional calculus.

Predicate Calculus (Alternative names: predicate logic, first order logic, elementary logic, restricted predicate calculus, restricted functional calculus, relational calculus, theory of quantification,

### Data Analysis 1. SET08104 Database Systems. Copyright @ Napier University

Data Analysis 1 SET08104 Database Systems Copyright @ Napier University Entity Relationship Modelling Overview Database Analysis Life Cycle Components of an Entity Relationship Diagram What is a relationship?

### Introduction to Conceptual Modeling

Introduction to Conceptual Modeling Gabriela P. Henning INTEC (Universidad Nacional del Litoral - CONICET) 3000 - Santa Fe, Argentina 1 Introduction to Conceptual Modeling - Outline Motivating questions

### Normal Form vs. Non-First Normal Form

Normal Form vs. Non-First Normal Form Kristian Torp Department of Computer Science Aalborg Univeristy www.cs.aau.dk/ torp torp@cs.aau.dk September 1, 2009 daisy.aau.dk Kristian Torp (Aalborg University)

### Foundations of Information Management

Foundations of Information Management - WS 2012/13 - Juniorprofessor Alexander Markowetz Bonn Aachen International Center for Information Technology (B-IT) Data & Databases Data: Simple information Database:

### Formal Engineering for Industrial Software Development

Shaoying Liu Formal Engineering for Industrial Software Development Using the SOFL Method With 90 Figures and 30 Tables Springer Contents Introduction 1 1.1 Software Life Cycle... 2 1.2 The Problem 4 1.3

### Deterministic Discrete Modeling

Deterministic Discrete Modeling Formal Semantics of Firewalls in Isabelle/HOL Cornelius Diekmann, M.Sc. Dr. Heiko Niedermayer Prof. Dr.-Ing. Georg Carle Lehrstuhl für Netzarchitekturen und Netzdienste

### Chapter 6: Programming Languages

Chapter 6: Programming Languages Computer Science: An Overview Eleventh Edition by J. Glenn Brookshear Copyright 2012 Pearson Education, Inc. Chapter 6: Programming Languages 6.1 Historical Perspective

### GCE Computing. COMP3 Problem Solving, Programming, Operating Systems, Databases and Networking Report on the Examination.

GCE Computing COMP3 Problem Solving, Programming, Operating Systems, Databases and Networking Report on the Examination 2510 Summer 2014 Version: 1.0 Further copies of this Report are available from aqa.org.uk

### School of Computer Science

School of Computer Science Computer Science - Honours Level - 2014/15 October 2014 General degree students wishing to enter 3000- level modules and non- graduating students wishing to enter 3000- level

### Eastern Washington University Department of Computer Science. Questionnaire for Prospective Masters in Computer Science Students

Eastern Washington University Department of Computer Science Questionnaire for Prospective Masters in Computer Science Students I. Personal Information Name: Last First M.I. Mailing Address: Permanent

### Introduction to formal semantics -

Introduction to formal semantics - Introduction to formal semantics 1 / 25 structure Motivation - Philosophy paradox antinomy division in object und Meta language Semiotics syntax semantics Pragmatics

OCEB White Paper on Business Rules, Decisions, and PRR Version 1.1, December 2008 Paul Vincent, co-chair OMG PRR FTF TIBCO Software Abstract The Object Management Group s work on standards for business

### Mathematics Cognitive Domains Framework: TIMSS 2003 Developmental Project Fourth and Eighth Grades

Appendix A Mathematics Cognitive Domains Framework: TIMSS 2003 Developmental Project Fourth and Eighth Grades To respond correctly to TIMSS test items, students need to be familiar with the mathematics

### Chapter 2: Entity-Relationship Model. Entity Sets. " Example: specific person, company, event, plant

Chapter 2: Entity-Relationship Model! Entity Sets! Relationship Sets! Design Issues! Mapping Constraints! Keys! E-R Diagram! Extended E-R Features! Design of an E-R Database Schema! Reduction of an E-R