Complexly fractionated syllogistic quantifiers

Consider syllogisms in which fraction (percentage) quantifiers are permitted in addition to universal and particular quantifiers, and then include further quantifiers which are modifications of such fractions (such as “almost 1/2 the S are P” and “Much more than 1/2 the S are P”). Could a syllogistic system containing such additional categorical forms be coherent? Thompson's attempt (1986) to give rules for determining validity of such syllogisms has failed; cf. Carnes &; Peterson (forthcoming) for proofs of the unsoundness and incompleteness of Thompson's rules. Building on Peterson (1985), the coherence of such a syllogistic can, however, be demonstrated with an algebra which provides its semantics; e.g., “almost 1/2 the S are P” is represented as “?(3(SP)?SP)”.