Chapter 8 Identity and Function Symbols

1 / 4

# Chapter 8 Identity and Function Symbols - PowerPoint PPT Presentation

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.

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

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

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 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
• 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)
• n. c = c =I
• Example:
• Show for all x, x = x
• |Show a = a, for any a
• | | a = a =I
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.