variables
play

Variables Variables are universally quantified in the scope of a - PowerPoint PPT Presentation

Apr 21, 2023 •24 likes •244 views

Variables Variables are universally quantified in the scope of a clause. A variable assignment is a function from variables into the domain. Given an interpretation and a variable assignment, each term denotes an individual and each clause is

  1. Variables Variables are universally quantified in the scope of a clause. A variable assignment is a function from variables into the domain. Given an interpretation and a variable assignment, each term denotes an individual and each clause is either true or false. A clause containing variables is true in an interpretation if it is true for all variable assignments. � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 1

  2. Queries and Answers A query is a way to ask if a body is a logical consequence of the knowledge base: ? b 1 ∧ · · · ∧ b m . An answer is either an instance of the query that is a logical consequence of the knowledge base KB , or no if no instance is a logical consequence of KB . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 2

  3. Example Queries  in ( kim , r 123) .  KB = part of ( r 123 , cs building ) . in ( X , Y ) ← part of ( Z , Y ) ∧ in ( X , Z ) .  Query Answer ? part of ( r 123 , B ) . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 3

  4. Example Queries  in ( kim , r 123) .  KB = part of ( r 123 , cs building ) . in ( X , Y ) ← part of ( Z , Y ) ∧ in ( X , Z ) .  Query Answer ? part of ( r 123 , B ) . part of ( r 123 , cs building ) ? part of ( r 023 , cs building ) . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 4

  5. Example Queries  in ( kim , r 123) .  KB = part of ( r 123 , cs building ) . in ( X , Y ) ← part of ( Z , Y ) ∧ in ( X , Z ) .  Query Answer ? part of ( r 123 , B ) . part of ( r 123 , cs building ) ? part of ( r 023 , cs building ) . no ? in ( kim , r 023) . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 5

  6. Example Queries  in ( kim , r 123) .  KB = part of ( r 123 , cs building ) . in ( X , Y ) ← part of ( Z , Y ) ∧ in ( X , Z ) .  Query Answer ? part of ( r 123 , B ) . part of ( r 123 , cs building ) ? part of ( r 023 , cs building ) . no ? in ( kim , r 023) . no ? in ( kim , B ) . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 6

  7. Example Queries  in ( kim , r 123) .  KB = part of ( r 123 , cs building ) . in ( X , Y ) ← part of ( Z , Y ) ∧ in ( X , Z ) .  Query Answer ? part of ( r 123 , B ) . part of ( r 123 , cs building ) ? part of ( r 023 , cs building ) . no ? in ( kim , r 023) . no ? in ( kim , B ) . in ( kim , r 123) in ( kim , cs building ) � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 7

  8. Logical Consequence Atom g is a logical consequence of KB if and only if: g is a fact in KB , or there is a rule g ← b 1 ∧ . . . ∧ b k in KB such that each b i is a logical consequence of KB . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 8

  9. Debugging false conclusions To debug answer g that is false in the intended interpretation: If g is a fact in KB , this fact is wrong. Otherwise, suppose g was proved using the rule: g ← b 1 ∧ . . . ∧ b k where each b i is a logical consequence of KB . ◮ If each b i is true in the intended interpretation, this clause is false in the intended interpretation. ◮ If some b i is false in the intended interpretation, debug b i . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 9

  10. Electrical Environment outside power cb1 w5 s1 w1 circuit breaker cb2 s2 w2 w3 off s3 w0 switch on w6 w4 two-way p2 switch l1 light p1 l2 power outlet � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 10

  11. Axiomatizing the Electrical Environment % light ( L ) is true if L is a light light ( l 1 ) . light ( l 2 ) . % down ( S ) is true if switch S is down down ( s 1 ) . up ( s 2 ) . up ( s 3 ) . % ok ( D ) is true if D is not broken ok ( l 1 ) . ok ( l 2 ) . ok ( cb 1 ) . ok ( cb 2 ) . ? light ( l 1 ) . = ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 11

  12. Axiomatizing the Electrical Environment % light ( L ) is true if L is a light light ( l 1 ) . light ( l 2 ) . % down ( S ) is true if switch S is down down ( s 1 ) . up ( s 2 ) . up ( s 3 ) . % ok ( D ) is true if D is not broken ok ( l 1 ) . ok ( l 2 ) . ok ( cb 1 ) . ok ( cb 2 ) . ? light ( l 1 ) . = yes ⇒ ? light ( l 6 ) . = ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 12

  13. Axiomatizing the Electrical Environment % light ( L ) is true if L is a light light ( l 1 ) . light ( l 2 ) . % down ( S ) is true if switch S is down down ( s 1 ) . up ( s 2 ) . up ( s 3 ) . % ok ( D ) is true if D is not broken ok ( l 1 ) . ok ( l 2 ) . ok ( cb 1 ) . ok ( cb 2 ) . ? light ( l 1 ) . = yes ⇒ ? light ( l 6 ) . = no ⇒ ? up ( X ) . = ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 13

  14. Axiomatizing the Electrical Environment % light ( L ) is true if L is a light light ( l 1 ) . light ( l 2 ) . % down ( S ) is true if switch S is down down ( s 1 ) . up ( s 2 ) . up ( s 3 ) . % ok ( D ) is true if D is not broken ok ( l 1 ) . ok ( l 2 ) . ok ( cb 1 ) . ok ( cb 2 ) . ? light ( l 1 ) . = yes ⇒ ? light ( l 6 ) . = no ⇒ ? up ( X ) . = up ( s 2 ), up ( s 3 ) ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 14

  15. connected to ( X , Y ) is true if component X is connected to Y connected to ( w 0 , w 1 ) ← up ( s 2 ) . connected to ( w 0 , w 2 ) ← down ( s 2 ) . connected to ( w 1 , w 3 ) ← up ( s 1 ) . connected to ( w 2 , w 3 ) ← down ( s 1 ) . connected to ( w 4 , w 3 ) ← up ( s 3 ) . connected to ( p 1 , w 3 ) . ? connected to ( w 0 , W ) . = ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 15

  16. connected to ( X , Y ) is true if component X is connected to Y connected to ( w 0 , w 1 ) ← up ( s 2 ) . connected to ( w 0 , w 2 ) ← down ( s 2 ) . connected to ( w 1 , w 3 ) ← up ( s 1 ) . connected to ( w 2 , w 3 ) ← down ( s 1 ) . connected to ( w 4 , w 3 ) ← up ( s 3 ) . connected to ( p 1 , w 3 ) . ? connected to ( w 0 , W ) . = W = w 1 ⇒ ? connected to ( w 1 , W ) . = ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 16

  17. connected to ( X , Y ) is true if component X is connected to Y connected to ( w 0 , w 1 ) ← up ( s 2 ) . connected to ( w 0 , w 2 ) ← down ( s 2 ) . connected to ( w 1 , w 3 ) ← up ( s 1 ) . connected to ( w 2 , w 3 ) ← down ( s 1 ) . connected to ( w 4 , w 3 ) ← up ( s 3 ) . connected to ( p 1 , w 3 ) . ? connected to ( w 0 , W ) . = W = w 1 ⇒ ? connected to ( w 1 , W ) . = no ⇒ ? connected to ( Y , w 3 ) . = ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 17

  18. connected to ( X , Y ) is true if component X is connected to Y connected to ( w 0 , w 1 ) ← up ( s 2 ) . connected to ( w 0 , w 2 ) ← down ( s 2 ) . connected to ( w 1 , w 3 ) ← up ( s 1 ) . connected to ( w 2 , w 3 ) ← down ( s 1 ) . connected to ( w 4 , w 3 ) ← up ( s 3 ) . connected to ( p 1 , w 3 ) . ? connected to ( w 0 , W ) . = W = w 1 ⇒ ? connected to ( w 1 , W ) . = no ⇒ ? connected to ( Y , w 3 ) . = Y = w 2 , Y = w 4 , Y = p 1 ⇒ ? connected to ( X , W ) . = ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 18

  19. connected to ( X , Y ) is true if component X is connected to Y connected to ( w 0 , w 1 ) ← up ( s 2 ) . connected to ( w 0 , w 2 ) ← down ( s 2 ) . connected to ( w 1 , w 3 ) ← up ( s 1 ) . connected to ( w 2 , w 3 ) ← down ( s 1 ) . connected to ( w 4 , w 3 ) ← up ( s 3 ) . connected to ( p 1 , w 3 ) . ? connected to ( w 0 , W ) . = W = w 1 ⇒ ? connected to ( w 1 , W ) . = no ⇒ ? connected to ( Y , w 3 ) . = Y = w 2 , Y = w 4 , Y = p 1 ⇒ ? connected to ( X , W ) . = X = w 0 , W = w 1 , . . . ⇒ � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 19

  20. % lit ( L ) is true if the light L is lit lit ( L ) ← light ( L ) ∧ ok ( L ) ∧ live ( L ) . % live ( C ) is true if there is power coming into C live ( Y ) ← connected to ( Y , Z ) ∧ live ( Z ) . live ( outside ) . This is a recursive definition of live . � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 20

  21. Recursion and Mathematical Induction above ( X , Y ) ← on ( X , Y ) . above ( X , Y ) ← on ( X , Z ) ∧ above ( Z , Y ) . This can be seen as: Recursive definition of above : prove above in terms of a base case ( on ) or a simpler instance of itself; or Way to prove above by mathematical induction: the base case is when there are no blocks between X and Y , and if you can prove above when there are n blocks between them, you can prove it when there are n + 1 blocks. � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 21

  22. Limitations Suppose you had a database using the relation: enrolled ( S , C ) which is true when student S is enrolled in course C . You can’t define the relation: empty course ( C ) which is true when course C has no students enrolled in it. This is because empty course ( C ) doesn’t logically follow from a set of enrolled relations. There are always models where someone is enrolled in a course! � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 12.3, Page 22

Recommend

Closures & Scoping Variables Parameters Local variables Free variables

Closures & Scoping Variables Parameters Local variables Free variables

CS152 Programming Language Paradigms Prof. Tom Austin, Fall 2016 Closures & Scoping Variables Parameters Local variables Free variables Variables not defined in the current scope e.g. global variables #!/bin/bash Is x

569 views • 13 slides
YCL Week 3 Lets talk about variables! Variables Variables are containers for data. Variables

YCL Week 3 Lets talk about variables! Variables Variables are containers for data. Variables

YCL Week 3 Lets talk about variables! Variables Variables are containers for data. Variables have two parts: a name and a value, which is of a certain data type. A variables value is usually assigned to it using an equal sign. x = 5

171 views • 15 slides
Runtime - Variables Storage and Access of Variables Three types of data memory (variables)

Runtime - Variables Storage and Access of Variables Three types of data memory (variables)

Todays Topic Runtime - Variables Storage and Access of Variables Three types of data memory (variables) Globals , locals , and dynamic/heap (new) Focus on first two for now How does compiler manage allocation of, reading of, and

565 views • 10 slides
Control Charts for Variables Terminology Variables refers to quantitative variables, like

Control Charts for Variables Terminology Variables refers to quantitative variables, like

ST 435/535 Statistical Methods for Quality and Productivity Improvement / Statistical Process Control Control Charts for Variables Terminology Variables refers to quantitative variables, like physical dimensions, as opposed to

264 views • 12 slides
CSS CUSTOM PROPERTIES (VARIABLES) What CSS Variables are? CSS variables are entities defined by

CSS CUSTOM PROPERTIES (VARIABLES) What CSS Variables are? CSS variables are entities defined by

CSS CUSTOM PROPERTIES (VARIABLES) What CSS Variables are? CSS variables are entities defined by CSS authors that contain specific values to be reused throughout a document. How to use a variable? --my-variable var(--my-variable); BENEFITS

453 views • 9 slides
Variables in C++ The variable C++ Variables Kinds of Variables Memory storage

Variables in C++ The variable C++ Variables Kinds of Variables Memory storage

Variables in C++ The variable C++ Variables Kinds of Variables Memory storage Variable qualifiers The variable The variable A variable declaration is a request for space Basic data types in memory int , short,

239 views • 6 slides
Discrete Random Variables October 7, 2010 Discrete Random Variables Random Variables In many

Discrete Random Variables October 7, 2010 Discrete Random Variables Random Variables In many

Discrete Random Variables October 7, 2010 Discrete Random Variables Random Variables In many situations, we are interested in numbers associated with the outcomes of a random experiment. For example: Testing cars from a production line, we are

489 views • 38 slides
4 Sums of Random Variables Many of the variables dealt with in physics can be expressed as a sum

4 Sums of Random Variables Many of the variables dealt with in physics can be expressed as a sum

47 Sums of a Random Variables 4 Sums of Random Variables Many of the variables dealt with in physics can be expressed as a sum of other variables; often the components of the sum are statistically indepen- dent. This section deals

378 views • 21 slides
Variables Motivation This series introduces the concept of variables Very powerful

Variables Motivation This series introduces the concept of variables Very powerful

Module 2 Variables Motivation This series introduces the concept of variables Very powerful programming concept Necessary for more complex Python features But variables can be tricky to work with With expressions, we got a value

947 views • 17 slides
Variables & References Variables with primitive types: Primitive types Lower

Variables & References Variables with primitive types: Primitive types Lower

Variables & References Variables with primitive types: Primitive types Lower case names int, float, double, boolean, Declare variables: <type name> <variableName>; Memory will be allocated to

399 views • 12 slides
Coded variables Some variables can be represented on different scales. E.g., temperature in

Coded variables Some variables can be represented on different scales. E.g., temperature in

ST 430/514 Introduction to Regression Analysis/Statistics for Management and the Social Sciences II Coded variables Some variables can be represented on different scales. E.g., temperature in degrees Celsius or Fahrenheit. Suppose some response

514 views • 23 slides
Structured Variables Marco Chiarandini Department of Mathematics & Computer Science

Structured Variables Marco Chiarandini Department of Mathematics & Computer Science

DM841 Discrete Optimization Part II Lecture 13 Structured Variables Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark Set Variables Graph Variables Resume and Outlook Float Variables

632 views • 45 slides
Set Variables Marco Chiarandini Department of Mathematics & Computer Science University of

Set Variables Marco Chiarandini Department of Mathematics & Computer Science University of

DM841 D ISCRETE O PTIMIZATION Part I Set Variables Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark Set Variables Graph Variables Resume and Outlook Float Variables Modeling in CP

462 views • 45 slides
Unit 4a Variables and 'cin' 2 Unit Objectives Know how variables are declared and assigned

Unit 4a Variables and 'cin' 2 Unit Objectives Know how variables are declared and assigned

1 Unit 4a Variables and 'cin' 2 Unit Objectives Know how variables are declared and assigned Use cin statement to get keyboard input from the user Predict how cin will treat input with whitespaces and extract data 3 VARIABLES

532 views • 19 slides
Lecture 5/Chapter 5 Experiments Variables Roles Outside Variables Single- or

Lecture 5/Chapter 5 Experiments Variables Roles Outside Variables Single- or

Lecture 5/Chapter 5 Experiments Variables Roles Outside Variables Single- or Double-Blind Experiments Flaws and Remedies in Experiments Roles of variables Most statistical studies of relationships attempt to establish evidence

763 views • 32 slides
CSS Variables @guilh https://sass-lang.com/guide http://lesscss.org/features/#variables-feature

CSS Variables @guilh https://sass-lang.com/guide http://lesscss.org/features/#variables-feature

The Power and Flexibility of CSS Variables @guilh https://sass-lang.com/guide http://lesscss.org/features/#variables-feature https://caniuse.com/#feat=css-variables CSS variables hold references to values you can reuse --property-name:

605 views • 39 slides
Data elements and bindings Variables and their values Expression (value) evaluation

Data elements and bindings Variables and their values Expression (value) evaluation

Imperative programming Data elements and bindings Variables and their values Expression (value) evaluation Binding of variables and types static and dynamic binding Lifetime of variables Scopes of variables Lambdas in

691 views • 45 slides
Preliminaries 32 / 384 Random variables Let V = { V 1 , . . . , V n } , n 1 , be a set of

Preliminaries 32 / 384 Random variables Let V = { V 1 , . . . , V n } , n 1 , be a set of

Chapter 2: Preliminaries 32 / 384 Random variables Let V = { V 1 , . . . , V n } , n 1 , be a set of random variables. Each variable V i V can take on one of m 2 values; for now we consider 2-valued variables: V i = true ,

992 views • 56 slides
Pointers and Variables Introduction to Programming and Computer Architecture Cs variables

Pointers and Variables Introduction to Programming and Computer Architecture Cs variables

Pointers and Variables Introduction to Programming and Computer Architecture Cs variables have a data type, e.g. int or double Revision Lectures This tells the compiler how much memory to put aside for it, and the rules for

275 views • 3 slides
Prophecy Variables in Separation Logic (Extending Iris with Prophecy Variables) Ralf Jung,

Prophecy Variables in Separation Logic (Extending Iris with Prophecy Variables) Ralf Jung,

Prophecy Variables in Separation Logic (Extending Iris with Prophecy Variables) Ralf Jung, Rodolphe Lepigre , Gaurav Parthasarathy, Marianna Rapoport, Amin Timany, Derek Dreyer, Bart Jacobs 1/18 What is Iris?! What are prophecy variables?! The

431 views • 18 slides
8/27/15 World Variables in a programming Hello Hello World language n Variables store

8/27/15 World Variables in a programming Hello Hello World language n Variables store

8/27/15 World Variables in a programming Hello Hello World language n Variables store information n You can think of them like boxes Basic Computation n They hold values (Savitch, Chapter 2) n The value of a variable is its

574 views • 19 slides
Variable Screening You will often have many candidate variables to use as independent variables

Variable Screening You will often have many candidate variables to use as independent variables

ST 430/514 Introduction to Regression Analysis/Statistics for Management and the Social Sciences II Variable Screening You will often have many candidate variables to use as independent variables in a regression model. Using all of them may be

266 views • 22 slides
Review Exam 1 Reading: textbook chapters 1, 2, 3.3, 4(4.1, 4.2, 4.3), 6, 7, 8 (1) Java

Review Exam 1 Reading: textbook chapters 1, 2, 3.3, 4(4.1, 4.2, 4.3), 6, 7, 8 (1) Java

Review Exam 1 Reading: textbook chapters 1, 2, 3.3, 4(4.1, 4.2, 4.3), 6, 7, 8 (1) Java primitive types, loops, conditionals instance variables, parameters, local variables, static variables scope of variables classes and objects;

87 views • 4 slides
Topic 4 Variables Once a programmer has understood the use of variables, he has understood

Topic 4 Variables Once a programmer has understood the use of variables, he has understood

Topic 4 Variables Once a programmer has understood the use of variables, he has understood the essence of programming - Edsger Dijkstra Edsger Dijkstra Based on slides for Building Java Programs by Reges/Stepp, found at

652 views • 35 slides

More recommend