Sentence examples for elimination theorem from inspiring English sources

To eliminate the middle term in a syllogism Boole borrowed an elimination theorem from ordinary algebra, but it was too weak for his algebra of logic.

The elimination theorem is discussed.

Later he took a particular interest in the quest for an Elimination Theorem in the calculus of classes.

The first volume concerned the equational logic of classes, the main result being Boole's Elimination Theorem of 1854.

Aside from the Rule of 0 and 1 and the Elimination Theorem, the 1854 presentation is mainly interesting for Boole's attempts to justify his algebra of logic.

In succeeding chapters he gave the Expansion Theorem, the new full-strength Elimination Theorem, a Reduction Theorem, and the use of division to solve an equation.

In particular, elimination theorems in the algebra of logic influenced decision procedures for fragments of first-order and second-order logic (see Mancosu, Zach, Badesa 2009).

Hacking shows that, given certain background semantic assumptions (bivalence, valid inference preserves truth), any introduction and elimination rules meeting certain proof-theoretic conditions (subformula property, provability of elimination theorems for Cut, Identity, and Weakening) will uniquely determine a semantics for the constant they govern (Hacking 1979, 311 314).

On the proof-theoretic side, a cut-elimination theorem for a sequent presentation of DL establishes decidability.

We aim for an implementation enabling us to formalise, within the logical framework, proof-theoretic results such as the cut-elimination theorem for δRA, and any associated increase in proof length.

The dead-end elimination (DEE) theorems are powerful tools for the combinatorial optimization of protein side-chain placement in protein design and homology modeling.