Sentence examples for as usually formulated from inspiring English sources

Thus, ∼M12 ∨... ∨ ∼M89 is a tautology, and this remains true if 1, 2,..., 9 are replaced by variables, such as r, s,..., z; hence, ∼Mrs ∨... ∨ ∼Myz, being a tautology expressed in the predicate calculus as usually formulated, is a theorem in it.

As a consequence, foundation, as usually formulated, can not be part of a ZF set theory based on intuitionistic logic.

As usually formulated, the argument from evil is based on what appears to be a false presumption.

As it is usually formulated, the objectives of the people are defined by the preferences of the majority.

Or, as it is usually formulated, a point in the plane is mapped onto a couple of real numbers, its coordinates.

As they are usually formulated, they include among the logical axioms the equality axioms, which state that equality, =, is reflexive and that equal terms can be substituted for one another in any formula.

OPV is usually formulated as a trivalent product, but monovalent OPV (mOPV) formulations for each serotype (mOPV1, mOPV2, and mOPV3) were used in the United States from 1961 to 1964, and both monovalent (primarily mOPV1) and bivalent formulations have been used in other countries since the 1960s 199).

Indeed, as we will see later on, arguments about qualia and consciousness are usually formulated as arguments for the conclusion that physicalism is false.

This type of measurements is usually formulated as the solution of inverse heat transfer problems.

The reliability constraints are usually formulated as constraints on the probability of failure.

The network design problem is usually formulated as a bi-level program, assuming the user equilibrium is attained in the lower level program.