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Logic and truth: Some logics without theorems

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Author(s): Jayanta Sen | Mihir Kumar Chakraborty

Journal: Studia Philosophica Estonica
ISSN 1406-0000

Volume: 1.1;
Start page: 104;
Date: 2008;
Original page

Keywords: logical truth | logical consequence | lattice

ABSTRACT
Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is inessential in order to define validity of an argument.
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