deducibility

Bolzano uses the word deducibility (Ableitbarkeit, literally derivability, but it is a sort of semantical relation).

Bolzano's Logic Sebestik, Jan 2007

Even earlier, C.I. Lewis started the modern study of modal logic by introducing strict implication as a kind of deducibility, where he may have meant deducibility in a formal system like Principia Mathematica, but this is not clear from his writings.

Provability Logic L.C. 2003

This recalls the way in which classical geneticists related gene differences and trait differences in the differential gene concept, where trait differences were used as markers for genetic differences without implying a deducibility of trait behavior, the dominance or recessivity of traits in particular, from Mendelian laws (Schwartz 2000; Falk 2001).

Gene Rheinberger, Hans-Jörg 2009

In exact deducibility the conclusion cannot be deduced from any proper subset of the premises.

Bolzano's Logic Sebestik, Jan 2007

The result is the concept of exact or strict, adequate, irredundant deducibility [genaue, genau bemessene Ableitbarkeit] or deducibility in the narrower sense, where there are no idle elements.

Bolzano's Logic Sebestik, Jan 2007

This deducibility requirement was intended to capture the idea that the explanatory principles (or laws) of the reducing theory ought to explain the explanatory principles (or laws) of the reduced theory.

Molecular Genetics Waters, Ken 2007

However, Lewis (Lewis and Langford 1932) replied in SL that these alleged paradoxes are simply the result of entirely natural assumptions about valid deductive inference and entailment quite apart from the systems of strict implication, and thus are not a problem for the claim that strict implication provides an explication of deducibility and entailment.

Clarence Irving Lewis Hunter, Bruce 2007

Exact deducibility requires that all the premises and all the ideas contained in them are necessary to draw the conclusion; this condition is the translation into logical terms of the condition of analytic proofs.

Bolzano's Logic Sebestik, Jan 2007

Let be the deducibility predicate corresponding in the language of propositional dynamic logic to the least normal modal logic containing every instance of the following axiom schemas:

Propositional Dynamic Logic Balbiani, Philippe 2007

The next example shows logical deducibility where the only invariable ideas are logical concepts:

Bolzano's Logic Sebestik, Jan 2007