Consequence mining: constants versus consequence relations

• The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside X, yields a function mapping X to a consequence relation =>_X. We investigate a function going in the other direction, thus extracting the constants of a given consequence relation, and we show that this function (a) retrieves the usual logical constants from the usual logical consequence relations, and (b) is an inverse to—more precisely, forms a Galois connection with—the Bolzano–Tarski function.

Subject headings

HUMANIORA  -- Filosofi, etik och religion -- Filosofi (hsv//swe)

HUMANITIES  -- Philosophy, Ethics and Religion -- Philosophy (hsv//eng)

Keyword

Consequence relation

Constant

Logical constant

Bolzano

Tarski

Galois connection

Replacement

Substitution

Publication and Content Type

ref (subject category)

art (subject category)