syntax of first order predicate calculus fopc 1 alphabet
Download
Skip this Video
Download Presentation
Syntax of First-Order Predicate Calculus (FOPC): 1. Alphabet

Loading in 2 Seconds...

play fullscreen
1 / 26

Syntax of First-Order Predicate Calculus FOPC: 1. Alphabet - PowerPoint PPT Presentation


  • 113 Views
  • Uploaded on

Syntax of First-Order Predicate Calculus (FOPC): 1. Alphabet. Countable set of predicate symbols , each with specified arity  0. Countable set of function symbols , each with specified arity  0. Function symbols with arity 0 are also called constants or individual 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 'Syntax of First-Order Predicate Calculus FOPC: 1. Alphabet' - dacey


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
syntax of first order predicate calculus fopc 1 alphabet
Syntax of First-Order Predicate Calculus (FOPC): 1. Alphabet
  • Countable set of predicate symbols, each with specified arity  0.
  • Countable set of function symbols, each with specified arity  0. Function symbols with arity 0 are also called constants or individual symbols.
  • Countable set of variables.
1 alphabet continued
1. Alphabet (Continued)
  • (Consistent with Prolog, we will begin variables with an upper-case letter and predicate/function symbols with a lower-case letter.)
  • Logical symbols: ,,,,,,
2 terms
2. Terms
  • A variable is a term.
  • If f is a function symbol of arity n and t1,…,tn are terms then f(t1,…,tn) is a term.
examples of terms
Examples of Terms
  • 0
  • s(s(s(0)))
  • nil
  • cons(1,nil)
  • cons(1,cons(2,nil))
  • cons(1,cons(2,cons(3,nil)))
3 formulas
3. Formulas
  • If p is a predicate symbol of arity n and t1,…,tn are terms, then p(t1,…,tn) is an atomic formula.
  • If a and b are formulas then so are a, ab, ab, ab, ab, ab.
  • If X is a variable and a is a formula then Xa and Xa are formulas. We say that X is quantified in the formulas Xa and Xa.
some notes
Some Notes
  • Predicates of arity 0 are also called propositions, the only atomic formulas allowed in propositional logic.
  • An expression is a term or formula. A formula with no free (unquantified) variables is a sentence.
slide17

Example: Models

X(Y((mother(X)  child_of(Y,X))  loves(X,Y)))

mother(mary)

child_of(tom,mary)

ad