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The argument for this conclusion turns on the notion of a conservative extension of a theory.
Compact bilinear logic is not a conservative extension of the original Syntactic Calculus.
The system C is a conservative extension of positive intuitionistic logic.
Reichenbach's probability logic is a conservative extension of classical first-order logic to include rules for probability implications.
For instance, some methods may require L to be the least conservative extension of both L1 and L2.
The addition of ∣− is (also) a conservative extension of FOL, and every occurrence of ∣− can be eliminated.
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Third, axioms of a scientific theory are not conservative extensions of the observation language since they enable us to make predictions.
Possibilistic versions of situation semantics are conservative extensions of possible worlds semantics that construe propositions as sets of world parts, rather than complete possible worlds (see Barwise 1988, chapter 11, for an overview of the major branch points in situation semantics).
We also present a non-conservative extension of the broken-triangle property which is also sufficient to ensure tractability and can also be detected in polynomial time.
We may conclude that while yielding a non-conservative extension of a favoured proof system is sufficient to denying the existence or intelligibility of a connective with such-and-such logical properties, there may be other grounds for returning such a verdict.
Here, the epsilon theorems no longer hold, i.e., introduction of epsilon terms produces non-conservative extensions of intuitionistic logic.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com