Game Description Logic with Integers: A GDL Numerical Extension

Many problems can be viewed as games, where one or more agents try to ensure that certain objectives hold no matter t he behavior from the environment and other agents. In recent years, a num ber of logical formalisms have been proposed for specifying games amo ng which the Game Description Language (GDL) was established as the o fficial language for General Game Playing. Although numbers are rec urring in games, the description of games with numerical features in G DL requires the enumeration from all possible numeric values and the rel ation among them. Thereby, in this paper, we introduce the Game Descript ion Logic with Integers (GDLZ) to describe games with numerical varia bles, numerical parameters, as well as to perform numerical compari sons. We compare our approach with GDL and show that when describing t he same game, GDLZ is more compact.