derivability

Recall that a translation from a logic L into a logic L² is a mapping f between the respective sets of formulas which preserves derivability, that is:

Combining Logics Carnielli, Walter 2007

Also, (6), together with (4), implies that the notion of derivability is complete with respect to logical truth (the second implication in (5)) and hence offers an extensionally correct characterization of this notion.

Logical Truth Gómez-Torrente, Mario 2006

Nevertheless, Frege's conception of logic has the result that there is only a one-way connection between logical implication as this holds between thoughts and formal derivability as this holds between sentences.

The Frege-Hilbert Controversy Blanchette, Patricia 2009

By invertibility, the question of derivability is replaced by one or two equivalent questions of derivability on simpler sequents.

Chores 2009

˜Ableitbarkeit™ (˜derivability™) is used nowadays in a purely syntactical sense, we use here instead the more common phrases ˜s follows from σ with respect to i™ or ˜s is a consequence of

Slices of Matisse gerard varni 2009

In short, because considerable logical complexity can lie undiscovered in the thoughts expressed by relatively-simple sentences, non-derivability is no guarantee of independence, in the Fregean scheme of things.

The Frege-Hilbert Controversy Blanchette, Patricia 2009

Sequent calculus, SC for short, can be seen as a formal representation of the derivability relation in natural deduction.

Chores 2009

So there is a pragmatic argument available that recommends the autonomy of social facts based on the infeasibility of derivability.

Arguments for social holism Daniel Little 2008

So there is a pragmatic argument available that recommends the autonomy of social facts based on the infeasibility of derivability.

Archive 2008-06-01 Daniel Little 2008

However, if TB contains scientific terms that do not occur in the language of the reducing theory TA (“organismal reproduction” is not an expression of biochemistry), derivability presupposes that the primitive expressions of TB (in particular its predicates) can be logically related to the language of

Reductionism in Biology Brigandt, Ingo 2008