Bolzano uses the word deducibility (Ableitbarkeit, literally derivability, but it is a sort of semantical relation). From Wordnik.com. [Bolzano's Logic] Reference
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. From Wordnik.com. [Provability Logic] Reference
Again, we define the deducibility relation by recursion. From Wordnik.com. [Classical Logic] Reference
Validity is the model-theoretic counterpart to deducibility. From Wordnik.com. [Classical Logic] Reference
It must not be confused with the purely logical relation of deducibility. From Wordnik.com. [Bolzano's Logic] Reference
The relation of deducibility in the general sense holds between the premise. From Wordnik.com. [Bolzano's Logic] Reference
Tarski's concept of logical consequence is close to Bolzano's logical deducibility. From Wordnik.com. [Bolzano's Logic] Reference
In exact deducibility the conclusion cannot be deduced from any proper subset of the premises. From Wordnik.com. [Bolzano's Logic] Reference
The next example shows logical deducibility where the only invariable ideas are logical concepts. From Wordnik.com. [Bolzano's Logic] Reference
On a view like this, deducibility and validity represent idealizations of correct reasoning in natural language. From Wordnik.com. [Classical Logic] Reference
What do deducibility and validity, as sharply defined on the addendum, tell us about correct reasoning in general?. From Wordnik.com. [Classical Logic] Reference
Bolzano tried to refine the concept of deducibility in adapting it to the then-current inferential practices in science. From Wordnik.com. [Bolzano's Logic] Reference
In the general case, Bolzano's deducibility is a triadic relation between the premises, the conclusion and the variable ideas. From Wordnik.com. [Bolzano's Logic] Reference
How do deducibility and validity, as properties of formal languages -- sets of strings on a fixed alphabet -- relate to correct reasoning?. From Wordnik.com. [Classical Logic] Reference
Nevertheless, fundamentally, Bolzano's deducibility is a semantic notion because it operates with the idea of “making true a propositional form”. From Wordnik.com. [Bolzano's Logic] Reference
Hence there are two kinds of grounding: formal grounding that is at the same time deducibility and material grounding that holds without deducibility. From Wordnik.com. [Bolzano's Logic] Reference
On a view like this, deducibility and validity represent mathematical models of (perhaps different aspects of) correct reasoning in natural languages. From Wordnik.com. [Classical Logic] Reference
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. From Wordnik.com. [Bolzano's Logic] Reference
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. From Wordnik.com. [Bolzano's Logic] Reference
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. From Wordnik.com. [Propositional Dynamic Logic] Reference
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. From Wordnik.com. [Bolzano's Logic] Reference
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. From Wordnik.com. [Molecular Genetics] Reference
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. From Wordnik.com. [Bolzano's Logic] Reference
If we take into account not the initial Bolzanian concept of deducibility relative to given variable ideas, but logical derivability, and either adapt or cancel the requirement of consistency of the premises, the distance seems rather short. From Wordnik.com. [Bolzano's Logic] Reference
Beyond that, what actually had failed was the attempt to characterize for natural languages the class of cognitively significant propositions by recursive definitions in purely logical terms, either by relations of deducibility or translatability. From Wordnik.com. [Vienna Circle] Reference
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). From Wordnik.com. [Gene] Reference
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. From Wordnik.com. [Clarence Irving Lewis] Reference
The solution is 100% deducibility for medical expenses. From Wordnik.com. [To The Point News Syndicated] Reference
In order to maintain the validity of interest expense deducibility, as well as the legitimacy of the concentration transactions, it is critical that any thin capitalisation (also referred to as the debt-to-equity ratio) limitations relating to individual participants are carefully considered. From Wordnik.com. [FinanceAsia] Reference
However, as noted above in discussion of the How question, nonreductive physicalists reply by agreeing that some account of psycho-physical realization is indeed needed, but adding that the relevant account may fall far short of a priori deducibility, yet still suffice to satisfy our legitimate explanatory demands (McGinn. From Wordnik.com. [Consciousness] Reference
The goal is to define a deducibility predicate. From Wordnik.com. [Propositional Dynamic Logic] Reference
6.5 Exact deducibility. From Wordnik.com. [Bolzano's Logic] Reference
(“proposition”, “deducibility”. From Wordnik.com. [Bolzano's Logic] Reference
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