material implication

[kylefoley76]

For those of you who know propositional logic, this is the material implication rule, which takes

(p) -> (q)

and turns it into

~(p) v (q)

I have two problems. In one function I'd like the t in "t as long" to be replaced with the hex character:
21FE

But I won't always be using the hex character so for now I would also like to use the > to stand for the t "t as long". I couldn't get > to work so I just used t.

unction matim(ByVal S As String) As String
  Dim X As Long, t As Long, Total As Long
  t = InStr(1, S, "t", vbTextCompare)
  
  For X = InStrRev(S, ")", t) To 1 Step -1
    If Mid(S, X, 1) = ")" Then
      Total = Total + 1
    ElseIf Mid(S, X, 1) = "(" Then
      Total = Total - 1
    End If
    If Total = 0 Then
      S = Application.Replace(S, X, 0, "~")
      Exit For
    End If
  Next
  S = Replace(S, "t", "v", , , vbTextCompare)
  matim = S
End Function

 

[kylefoley76]

Ok, I figured out that the above algorithm can't handle multiple implications embedded in one sentence. For example it cannot transform

(((p v q) > (r v (p v q))) > ((p & s) v (r v s))) > (p & r)

into


~(~(~(p v q) v (r v (p v q))) v ((p & s) v (r v s))) v (p & r)

So it seems that the new algorithm should be:

1. start with the left most character, go right, look for >, when the first > is found, go left and count the open and closed parentheses, when the open and closed parentheses equal each other then replace the open parentheses that eventually equaled the amount of closed parentheses with ~(
2. then return to the first > found, then go right and look for another > and repeat the procedure until all > have been transformed.

 

[kylefoley76]

anyone know this?

 

[shg]

Kyle, I'll weigh in, but only briefly.

You can't get there from here. You need to write a parser, build a parse tree, and a PL expression evaluator. You can't do it by counting parentheses.