chapter 8 identity and function symbols n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Chapter 8 Identity and Function Symbols PowerPoint Presentation
Download Presentation
Chapter 8 Identity and Function Symbols

Loading in 2 Seconds...

play fullscreen
1 / 4

Chapter 8 Identity and Function Symbols - PowerPoint PPT Presentation


  • 100 Views
  • Uploaded on

Chapter 8 Identity and Function Symbols. Mathematical functions, e.g., +, –, , δ Identity = (“is”) can be treated as either a dyadic predicate or a function: =(x,y), x=y Definition of Terms : Constants (in the book), combination of constants, and function symbols.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Chapter 8 Identity and Function Symbols' - thuong


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
chapter 8 identity and function symbols
Chapter 8Identity and Function Symbols
  • Mathematical functions, e.g., +, –, , δ
  • Identity = (“is”) can be treated as either a dyadic predicate or a function:

=(x,y), x=y

  • Definition of Terms: Constants (in the book), combination of constants, and function symbols.
functions and predicates
Functions and Predicates
  • Individual variables can be used to do substitutions: =(a, b) / =(x, y), for any a, b
  • “There is at least two Fs”:

xy(Fx & Fy & ≠(x, y))

Adding functions makes quantified predicate logic more powerful

identity introduction i
Identity Introduction (=I)
  • n. c = c =I
  • Example:
    • Show for all x, x = x
    • |Show a = a, for any a
    • | | a = a =I
identity elimination e
Identity Elimination (=E)
  • n. t = u

m. A

-------------------

p. A[t // u] or A[u // t] n, m, =E

Here A[t // u] is any result of substituting t for some or all occurrences of u throghout A.

e.g., A[c // d] could be: Fcd, Fdc, Fcc.