Predicate Logic and Quantifiers
Predicate Logic and Quantifiers CSE235
Introduction Propositional Functions Propositional Functions Quantifiers Logic Programming Transcribing English into Logic Further Examples & Exercises
1 / 33
Predicate Logic and Quantifiers
Slides by Christopher M. Bourke Instructor: Berthe Y. Choueiry
Fall 2007 Computer Science & Engineering 235 Introduction to Discrete Mathematics
Sections 1.3?1.4 of Rosen cse235@cse.unl.edu
Introduction
Predicate Logic and Quantifiers CSE235
Introduction Propositional Functions Propositional Functions Quantifiers Logic Programming Transcribing English into Logic Further Examples & Exercises
2 / 33
Consider the following statements:
x > 3, x = y + 3, x + y = z
The truth value of these statements has no meaning without specifying the values of x, y, z.
However, we can make propositions out of such statements.
A predicate is a property that is affirmed or denied about the subject (in logic, we say "variable" or "argument") of a statement.
" x is greater than 3"
subject
predicate
Terminology: affirmed = holds = is true; denied = does not hold = is not true.
Propositional Functions
Predicate Logic and Quantifiers CSE235
Introduction Propositional Functions Propositional Functions Quantifiers Logic Programming Transcribing English into Logic Further Examples & Exercises
3 / 33
To write in predicate logic:
" x is greater than 3"
subject
predicate
We introduce a (functional) symbol for the predicate, and put the subject as an argument (to the functional symbol): P (x)
Examples:
Father(x): unary predicate Brother(x,y): binary predicate Sum(x,y,z): ternary predicate P(x,y,z,t): n-ary predicate
Propositional Functions
Predicate Logic and Quantifiers
CSE235
Introduction
Propositional Functions
Propositional Functions Universe of Discourse
Quantifiers
Logic Programming
Transcribing English into Logic
Further Examples & Exercises
Definition
A statement of the form P (x1, x2, . . . , xn) is the value of the propositional function P . Here, (x1, x2, . . . , xn) is an n-tuple and P is a predicate.
You can think of a propositional function as a function that
Evaluates to true or false. Takes one or more arguments. Expresses a predicate involving the argument(s). Becomes a proposition when values are assigned to the arguments.
4 / 33
Propositional Functions
Example
Predicate Logic and Quantifiers
CSE235
Introduction
Propositional Functions
Propositional Functions Universe of Discourse
Quantifiers
Logic Programming
Transcribing English into Logic
Further Examples & Exercises
Example
Let Q(x, y, z) denote the statement "x2 + y2 = z2". What is the truth value of Q(3, 4, 5)? What is the truth value of Q(2, 2, 3)? How many values of (x, y, z) make the predicate true?
5 / 33
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- name date grammar quiz quantifiers some any
- chapter 8 quantifiers pcc
- quantifiers qu 1 fill in much many lots of a lot of
- quantifier worksheet 1 description quantifiers aims
- chapter1
- quantifiers determiners exercises grammarbank
- predicate logic and quantifiers
- name date grammar worksheet quantifiers
- some any much many a lot a few a little
- a little little a few few perfect english grammar
Related searches
- predicate logic proof solver
- predicate logic generator
- predicate logic natural deduction solver
- predicate logic practice problems
- predicate logic calculator
- predicate logic derivations solver
- predicate logic rules
- predicate logic laws
- predicate logic only one
- predicate logic wikipedia
- predicate logic examples
- predicate logic pdf