Local finiteness in t-norm bimonoids: Overlap cases

This paper offers a discussion of the property of local finiteness for t-norm bimonoids for continuous t-norms determined by ordinal sums of Łukasiewicz summands. Of particular interest are, besides the case of rational local finiteness, in general those cases where some definition intervals for such t-norm summands and t-conorm summands overlap. Some such bimonoids are of interest in the context of weighted automata. It will be proved that overlap destroys local finiteness.