Bolzano uses the word deducibility (Ableitbarkeit, literally derivability, but it is a sort of semantical relation). ❋ 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. ❋ 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). ❋ Rheinberger, Hans-Jörg (2009)
[α-1] A to the proof system of section 3, we obtain a sound and complete deducibility predicate in the extended language. ❋ Balbiani, Philippe (2007)
It must not be confused with the purely logical relation of deducibility. ❋ Sebestik, Jan (2007)
In exact deducibility the conclusion cannot be deduced from any proper subset of the premises. ❋ Sebestik, Jan (2007)
It is imbedded in the very foundations of his system and all other relations (with exception of different cases of disjunction, Bolzano 1837, § 160), deducibility included, are special cases of it. ❋ Sebestik, Jan (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. ❋ Hunter, Bruce (2007)
Hence there are two kinds of grounding: formal grounding that is at the same time deducibility and material grounding that holds without deducibility. ❋ Sebestik, Jan (2007)
The relation of deducibility in the general sense holds between the premise: ❋ 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: ❋ Balbiani, Philippe (2007)
In the general case, Bolzano's deducibility is a triadic relation between the premises, the conclusion and the variable ideas. ❋ Sebestik, Jan (2007)
Hafner (1999, 387) showed that indirect proofs are not related to compatibility requirement or the concept of deducibility, but only to the concept of grounding. ❋ 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. ❋ Sebestik, Jan (2007)
Nevertheless, fundamentally, Bolzano's deducibility is a semantic notion because it operates with the idea of “making true a propositional form”. ❋ 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. ❋ Waters, Ken (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. ❋ Sebestik, Jan (2007)
Grounding, being no more a simple concept and defined in terms of deducibility by the optimal partition between axioms and theorems, becomes a global property of a deductive theory. ❋ Sebestik, Jan (2007)
The next example shows logical deducibility where the only invariable ideas are logical concepts: ❋ Sebestik, Jan (2007)
Bolzano tried to refine the concept of deducibility in adapting it to the then-current inferential practices in science. ❋ Sebestik, Jan (2007)
"Man, [I pooped] this morning, but I still had to [drop] a [deduce] after work." ❋ MissR1992 (2015)
Generally speaking, parents possess more deducation than their children. But none [surpass] the deducation level displayed by [university] [presidents]. ❋ Deadeye111 (2016)
Your [communication] with this [skilled] group on this topic is pure [deducation]. If you continue deducate your members, they will end up knowing less. ❋ Sringstad (2019)
