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Can someone please explain the difference between formula in general and well-formed formula? Is it possible to determine the truth value of an ill-formed formula?

yeshika Senadeera
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The validity of a formula, or its truth value (or more generally its evaluation), can only be assessed if the formula is well formed with respect to a given set of syntax rules.

So a formula in general, and in the context of math or logic, means well-formed formula.

Strictly speaking, you can say that if your symbols include '+' | '(' | ')' | 'a'-'z', a formula, in the strict sense, is any string formed by these symbols. For example, a((++z is a formula.

But one must also look at the rules of construction of a formula. And if the rules are, for example

F,E ::= F + E | (F) | 'a'-'z'

then your formula is not well formed.

ZakC
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    ZakC is correct, but just to emphasise the point: there is almost no situation in logic when "formula" does not mean "well-formed formula". And in direct answer to the OP's second question: an ill-formed formula has no truth value. – MattClarke Mar 08 '16 at 00:12
  • Thank you @ZakC for your explaination – yeshika Senadeera Mar 09 '16 at 03:47