Recursive Definition of Formula Length: Learn the Basics | Logics Course Help

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SUMMARY

The discussion focuses on defining the recursive length of well-formed formulas (wffs) in logic. It establishes that the length of an atomic formula, such as 'p', is 1. The recursive rules outlined specify that if 'p' is a wff of length 'n', then the negation '~p' has a length of 'n + 3'. Additionally, when combining two wffs 'p' and 'q' of lengths 'n' and 'm', respectively, the conjunction '(p^q)' results in a length of 'm + n + 3'.

PREREQUISITES
  • Understanding of well-formed formulas (wffs) in logic
  • Familiarity with recursive definitions
  • Basic knowledge of logical operators such as negation and conjunction
  • Concept of atomic formulas in propositional logic
NEXT STEPS
  • Study recursive definitions in formal logic
  • Explore the properties of well-formed formulas in propositional logic
  • Learn about logical operators and their implications on formula length
  • Investigate examples of constructing complex wffs from atomic formulas
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Students in logic courses, educators teaching formal logic, and anyone interested in understanding the structure and length of logical expressions.

blackdvl666
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ok guys this is from my logics course!

this question may be very simple but i am just gettin stuck

give a recursive definition of the length of a well formed formula that is of the number of the symbols occurring in it. For example length of (p^(~q)) is 8.
 
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OK, so if p is an atomic formula, the length is 1.
What possibilities do you have to make a new wff out of two wffs p and q?
For example, if p is a wff of length n, then (~p) is one of length n + 3.
If p and q are wff's of length n and m, respectively, then (p^q) is of length m+n+3.
 

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