Friendliness for logicians

Abstract
We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is studied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.
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For Want of an 'And': A Puzzle About Non-Conservative Extension.Lloyd Humberstone - 2005 - History and Philosophy of Logic 26 (3):229-266.

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