Game Description Logic with Integers: A GDL Numerical Extension

TL;DR

This paper introduces GDLZ, an extension of GDL that incorporates integers for more compact and expressive game descriptions involving numerical variables and comparisons.

Contribution

The paper presents GDLZ, a novel logical formalism extending GDL to efficiently describe games with numerical features, improving compactness and expressiveness.

Findings

GDLZ is more compact than GDL for describing numerical games.

GDLZ allows direct numerical comparisons, simplifying game descriptions.

The approach enhances the expressiveness of game descriptions involving numbers.

Abstract

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.