Sentence examples for a deduction system from inspiring English sources

This serious problem opens the opportunity for a deduction system to provide a service to the computer algebra system: Use its deductive capabilities to verify that the computer algebra's computational steps meet the required assumptions.

We propose a deduction system which is described using a set of inference rules.

The diagnostic process is described by a deduction system that performs an abductive inference.

Let us call such a pair a logical deduction system, and the formulas derivable in the calculus the theorems of the system (nowadays it is common practice to refer to this kind of calculi as Hilbert style calculi).

Consider now another (even worse) situation: the logic L1 is described by semantical means (that is, through semantic structures such as valuations or Kripke models) whereas the logic L2 is presented through a syntactical proof system, such as a natural deduction system, sequent calculus or a Hilbert-style axiomatization.

Given a logical deduction system H the relation ⊢ defined by X ⊢ a if a is deducible from X in H is a finitary consequence relation.

Second, it introduces a minimalist deduction system over this fragment, which by avoiding certain rare cases, obtains a simple deductive system and a computationally efficient entailment checking.

See also Braüner and de Paiva (2006) where a natural deduction system is given for intuitionistic hybrid logic.

In the case of arbitrary n-ary propositional connectives this leads to a natural deduction system with generalized introduction and elimination rules.

The first influential attempts to introduce logics different from classical logic remained within the Frege-Russell tradition of presenting a logical deduction system without any formal semantics.

In the future, we expect that with further accumulated binary relationship data under a new deduction system, novel differentiation pathways will be explored and experimentally verified.