  In this paper the 3-valued paraconsistent first-order logic QCiore is studied
from the point of view of Model Theory. The semantics for QCiore is given by
partial structures, which are first-order structures in which each n-ary
predicate R is interpreted as a triple of paiwise disjoint sets of n-uples
representing, respectively, the set of tuples which actually belong to R, the
set of tuples which actually do not belong to R, and the set of tuples whose
status is dubious or contradictory. Partial structures were proposed in 1986 by
I. Mikenberg, N. da Costa and R. Chuaqui for the theory of quasi-truth (or
pragmatic truth). In 2014, partial structures were studied by M. Coniglio and
L. Silvestrini for a 3-valued paraconsistent first-order logic called LPT1,
whose 3-valued propositional fragment is equivalent to da Costa-D'Otaviano's
logic J3. This approach is adapted in this paper to QCiore, and some important
results of classical Model Theory such as Robinson's joint consistency theorem,
amalgamation and interpolation are obtained. Although we focus on QCiore, this
framework can be adapted to other 3-valued first-order logics.
