  We study the extension of relational multiagent systems (RMASs), where agents
manipulate full-fledged relational databases, with data types and facets
equipped with domain-specific, rigid relations (such as total orders).
Specifically, we focus on design-time verification of RMASs against rich
first-order temporal properties expressed in a variant of first-order
mu-calculus with quantification across states. We build on previous
decidability results under the "state-bounded" assumption, i.e., in each single
state only a bounded number of data objects is stored in the agent databases,
while unboundedly many can be encountered over time. We recast this condition,
showing decidability in presence of dense, linear orders, and facets defined on
top of them. Our approach is based on the construction of a finite-state, sound
and complete abstraction of the original system, in which dense linear orders
are reformulated as non-rigid relations working on the active domain of the
system only. We also show undecidability when including a data type equipped
with the successor relation.
