Sentence examples similar to trivial system of from inspiring English sources

Since classical propositional logic is Post-complete, any additional axiom in its language gives rise to the trivial system, so that any non-trivial system of connexive logic will have to leave out some theorems of classical logic.

Since every non-trivial system of connexive logic has to omit some classical tautologies, and since the standard paradoxes of non-relevant, material implication can be avoided by rejecting Conjunctive Simplification, i.e., (A ∧ B) → A and (A ∧ B) → B, Routley requires for a connexive logic the rejection or qualification of Conjunctive Simplification (or equivalent schemata).

are essential characteristics of any non-trivial system.

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

The fabrication of coplanar hybrid devices is a fundamental step to pave the way to the understanding of proximity effects in topologically non-trivial systems, and to a large variety of experiments aimed at the possible detection of MBS.

In order to show the exponential stability of the trivial solution of system (4), the system is solved numerically using the Euler method.

Hence, we see that the trivial solution of the linearized system of (1.2) about (E_{0}) is stable.

Definition 5. We call the equilibrium u* of system (17) is exponentially stable, if the trivial solution of system (18) is exponentially stable.

Obviously, the -stability analysis of the equilibrium point of system (2.1) can be transformed to the -stability analysis of the trivial solution of system (2.5).

If (bar{b}>0), then the solution of system (3) is positive recurrent and has a UEAID; if (bar{b}<0), then the trivial solution of system (3) is SGAS.

(ii)The trivial solution of system (3.13) is stable by Lyapunov (uniformly, if ). (iii) The trivial solution of system (3.13) is -stable by Chetaev (uniformly if is independent of ) and  .