  Many problems can be viewed as games, where one or more agents try to ensure
that certain objectives hold no matter the behavior from the environment and
other agents. In recent years, a number of logical formalisms have been
proposed for specifying games among which the Game Description Language (GDL)
was established as the official language for General Game Playing. Although
numbers are recurring in games, the description of games with numerical
features in GDL requires the enumeration from all possible numeric values and
the relation among them. Thereby, in this paper, we introduce the Game
Description Logic with Integers (GDLZ) to describe games with numerical
variables, numerical parameters, as well as to perform numerical comparisons.
We compare our approach with GDL and show that when describing the same game,
GDLZ is more compact.
