It is argued that the preservation of truth by an inference relation is of little interest when premiss sets are contradictory. The notion of a level of coherence is introduced and the utility of modal logics in the semantic representation of sets of higher coherence levels is noted. It is shown that this representative role cannot be transferred to first order logic via frame theory since the modal formulae expressing coherence level restrictions are not first order definable. Finally, an inference (...) relation, calledyielding, is introduced which is intermediate between the coherence preservingforcing relation introduced elsewhere by the authors and the coherence destroying, inference relation of classical logic. (shrink)

Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic of henceforth, next, and until, and to the propositional dynamic logic of regular programs.

Related Works: Original Paper: Peter Apostoli, Bryson Brown. A Solution to the Completeness Problem for Weakly Aggregative Modal Logic. J. Symbolic Logic, Volume 60, Issue 3, 832--842. Project Euclid: euclid.jsl/1183744808.