Logic and Truth: Some Logics without Theorems
DOI:
https://doi.org/10.12697/spe.2008.1.1.06Keywords:
logical truth, logical consequence, latticeAbstract
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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