Sentence examples for because the standard semantics from inspiring English sources

This is because the standard semantics for quantification is objectual: A quantified sentence ∃xΦx is true just in case there is an object that Φx is true of.

The standard semantics for modal logic revolves around possible worlds.

This is a stronger requirement than saying that σ is valid in the standard semantics.

Hence the standard semantics of FO is Tarski-type, but Hodges's semantics employing the satisfaction relation 'M ⊨X φ' is not, because the latter evaluates a formula φ x1,…, xn) of n free variables relative to an entire set of n-tuples of elements.

As a consequence, the data complexity of SWORL w.r.t. the standard semantics is in PTime.

The data complexity of SWORL with respect to the standard semantics is in PTime.

In the standard semantics, the only model of the Peano postulates, up to isomorphism, is the usual model of arithmetic.

When this is complete, the files will be re-parsed to reflect the standard semantics.

So the theory generated by these axioms (in the standard semantics) is simply the second-order theory of true arithmetic.

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

Both WORL with respect to the well-founded semantics and SWORL with respect to the standard semantics have PTime data complexity.