  In this paper, a new approximate syllogistic reasoning schema is described
that expands some of the approaches expounded in the literature into two ways:
(i) a number of different types of quantifiers (logical, absolute,
proportional, comparative and exception) taken from Theory of Generalized
Quantifiers and similarity quantifiers, taken from statistics, are considered
and (ii) any number of premises can be taken into account within the reasoning
process. Furthermore, a systematic reasoning procedure to solve the syllogism
is also proposed, interpreting it as an equivalent mathematical optimization
problem, where the premises constitute the constraints of the searching space
for the quantifier in the conclusion.
