Sentence examples for open formulas from inspiring English sources

The linguistic expressions which signify objectives are just open formulas like 'Px', 'Rxy', etc.

Notice (importantly) that open formulas are assertible as axioms and provable as theorems in SQML.

Open formulas are merely true or false under an assignment of values to their free variables.

(See Williamson (1999) for an illuminating discussion of problems engendered by permitting open formulas in inclusive logics).

Since an ordinary first-order language has a denumerable supply of open formulas, at most denumerably many sets (in any given domain) can be specified in this way.

(Note that free variables in open formulas— in a sense behave like name constants, and their elimination is neither intended, nor achieved in the procedures described here).

"Calling it a par-4 now immediately knocks four shots off the score relative to par," said Phil Mickelson, the American star still searching for the right British Open formula.

Or to put it another way: if the forbidden is essential to sexual excitement, and our culture dictates that almost nothing is forbidden except inequality, we are stuck with a compassionate and open formula that is morally admirable but all the same ensures dullness in the bedroom.

Are they "term-forming operators" which turn an open formula into a name for a function, or simply a syntactic device, a placeholder, for indicating the variable for which a substitution can made in an open formula?

To say that an open formula φ(x) is true of an individual a seems equivalent (in some sense) to the claim that a has the property of being such that φ (this property is signified by the open formula).

But now consider the substitution instance ~Pt → E t, in which the open formula ~Px is substituted for P.