Sentence examples for conservative extension from inspiring English sources
noun
An extension of a logical theory such that every theorem expressible in the original theory is also derivable within the original theory.
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.
The problem of applicability has to be met, by providing conservative extension proofs for example.
There is a natural notion of conservative extension which applies directly to (pairs of) consequence relations, but to avoid going into that here, we have adopted a formulation in terms of conservative extension as a relation between proof systems.
Reichenbach's probability logic is a conservative extension of classical first-order logic to include rules for probability implications.
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).
Older GPs are at increased risk of burn-out and may not be easily encouraged to continue in practice hence the choice of conservative extensions to working life.
For the four systems in the hierarchy, one writes (N L(P * for the (non-conservative) extension which allows empty antecedents.
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.
