Sentence examples for logic is valid from inspiring English sources

A logic formulated in a given language L* is said to be sound with respect to a semantics for L* if and only if every formula of L* that is a theorem of the logic is valid (logically true) relative to that semantics (i.e., is true in every interpretation or model of the semantics).

The former subject began with the work of Gödel, Church, Turing, Kleene, and Post originally undertaken during the 1930s in attempt to answer Hilbert's Entscheidungsproblem – i.e. is the problem \(\sc{FO}\text\sc{VALID}\) of determining whether a given formula of first-order logic is valid decidable?

Note that this logic is valid only if odor intensities are adjusted for equal learnability (the same caveat also applies to the tasks ii iv below).

Since the axioms of pure quantificational logic are valid and the rules of inference preserve validity, all theorems of pure quantificational logic are valid.

In fact, if we consider the standard reductions of intuitionistic logic, then all derivations in intuitionistic logic are valid independent of the atomic system considered.

Then, verifying if a set of properties, expressed in temporal logics, are valid in the designed model, using a model checker.

On the standard semantics for modal logic, if A is valid, then it is true at all possible worlds.

Second, and more moderately, most theologians insisted that Aristotelian logic is universal thus, valid in both the natural and supernatural realms but that the trinitarian syllogisms in question are not valid syllogisms, despite their seemingly valid form.

To phrase it for maximum shock value: sometimes when one logic says 'argument A is valid' and another says 'argument A is not valid', the logical pluralist judges that both are correct.

But, he said, that "this basic logic isn't valid in current circumstances" because banks were sitting on nearly $1 trillion in excess reserves held at the Fed.

Therefore, if φ is a second-order sentence and φ* its reconstruction in two-sorted first-order logic, we have: φ is valid iff (¬X ∨ φ*) is valid iff (Y ∨ φ*) is valid.