[FOM] Model theory for mereology, without sets?

[David NICOLAS]

Hello,

Mereology was conceived by Lesniewski as an alternative to set theory.
Mereology can be axiomatized in predicate logic (cf. e.g. Simons 
1987, Link 1998).

Now, we might want to have a model theory for mereology. Could one be 
developped without sets?
What I have in mind in something in the same spirit than this. 
Friends of first order plural logic (predicate logic augmented with 
plural quantifiers and plural predicates) have developped model 
theories for first order plural logic, using metalanguages that 
contains plurals, and without using sets.
Can something like this be done for mereology? Namely, develop a 
model theory for mereology in a suitable metalanguage, without using 
sets (nor plurals) to specify models? Is there some existing work on this?

References:
Simons, P. 1987. Parts. OUP.
Link, G. 1998. Algebraic semantics. CSLI.

Thanks,

David Nicolas