Sentence examples for inconsistent systems from inspiring English sources

Inconsistent systems can prove all statements and therefore are pretty useless.

Examples of non-trivial inconsistent systems of connexive logic satisfying Conjunctive Simplification are presented in Sections 2.4 and 2.5.

Extensive tests have shown that proceeding in this way inconsistent systems are quickly discovered and may be discarded.

(4) Next, there is the well-known case of inconsistent systems of linear equations, such as the system (i) x+y=1, plus (ii) x+y=2.

If formalising the intuitive, "naive" understanding of these subjects, inconsistent systems linger as the paradoxes will be formalisable in these systems.

The contribution is thus two-fold; unlike the standard Kaczmarz method, our results demonstrate convergence to the least squares solution of inconsistent systems (both methods in the nearly standardized case and the second method in other cases).

The current 140-year-old, inconsistent system of state-based regulation lacks the resources and expertise to oversee what has become a global insurance market.

"It's remarkable that in this day and age we have such an archaic and inconsistent system of recording deaths," said Louise Bazalgette, researcher at Demos.

But there is no reason that a machine or a mathematician cannot use an inconsistent system of logic to prove things like Gödel's theorem and even understand that, just as Gödel did.

This was due to hardware errors on some nodes, and inconsistent system software installations on others.

An easy consequence of Gentzen's version of the incompleteness theorem is the consistency of Peano arithmetic, because anything would be provable in an inconsistent system.