Saturday, June 15, 2013

Proposal: Expressions and quantifiers

Times out and passes 6-0 / Skju

Adminned at 17 Jun 2013 11:50:14 UTC

To the rule “Formulae”, add the following paragraphs (excluding text between square brackets):

An Identifier is a string of uppercase letters. [This would be called a Variable, but that name is already taken.] A Predicate is an uppercase letter followed by at least one lowercase letter.

A single Identifier is an Expression. An Identifier, followed by a list of Expressions enclosed in parentheses and separated by commas (e.g. “F(X,Y)”), is an Expression. A Predicate, followed by a list of Expressions enclosed in parentheses and separated by commas, is a Formula.

The symbols “FA” and “TE” are Quantifiers, not Identifiers. [“FA” represents the phrase “for all”, and “TE” represents “there exists”.] A Quantifier, followed by an Identifier, followed by a Formula, is a Formula.

Now we can have sentences referring to Atoms and whatnot without them having to be Formulas with truth values,

Comments

kikar:

16-06-2013 01:46:19 UTC

for Although, I’m not sure that you’ve defined expression well enough.

Skju:

16-06-2013 03:48:46 UTC

for What about a Quantifier followed by a Variable? And how not, Kikar?

quirck: he/him

16-06-2013 06:09:55 UTC

imperial

Tavros:

16-06-2013 17:45:08 UTC

Yeah, I guess a Quantifier followed by a Variable may be useful (although first-order logic doesn’t use them). You could simulate them by having the Boolean Identifiers T and F, and letting True(T) be True and True(F) be False,

nqeron:

17-06-2013 11:33:05 UTC

imperial

Wakukee:

17-06-2013 18:42:47 UTC

imperial