Sentence examples for deductive system from inspiring English sources

In order to give an account of this notion we wil introduce a deductive system (a natural deduction system), which explicate the intuitive notion of 'follow' in terms of derivational rules in a calculus.

Thus, if we can show that a given language is not (weakly) κ-compact, then there can be no deductive system for it with deductions of length < κ adequate for deductions from arbitrary sets of premises (of cardinality ≤ κ).

weakly κ-complete) if there is a deductive system P for L with deductions of length < κ such that, if Δ is a P-consistent[4] set of L-sentences (resp. such that |Δ| ≤ κ), then Δ has a model.

This establishes that the deductive system is rich enough to provide a deduction for every valid argument.

Thus, with some reservations, we might compare the perfect deductions to the axioms or primitive rules of a deductive system.

Section 3 sets up a deductive system for the language, in the spirit of natural deduction.

This fact, which Aristotle himself showed, makes his syllogistic the first deductive system in the history of logic.

The tablets indicate that the Mesopotamians had a great deal of remarkable mathematical knowledge, although they offer no evidence that this knowledge was organized into a deductive system.

The method treats theory as a deductive system in which particular empirical phenomena are explained by relating them back to general principles and definitions.

For this purpose they have taken a deductive system to require not just that the premises entail the conclusions but further that they themselves be necessarily true.

It is clear that metaphysical philosophers have sometimes aspired to present their results in the form of a deductive system, to make metaphysics an a priori science.