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.
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Notes
- 1.
Due to the space limitation, we omitted most of the Propositions and Theorems proofs. All the proofs are available at https://arxiv.org/abs/1912.01876.
- 2.
Through the rest of this paper, the functions minimum(a, b) and maximum(a, b) respectively return the minimum and maximum value between \(a,b \in \mathbb {Z}\).
- 3.
We say that \(\psi \) is a subformula of \(\varphi \in \mathcal {L}_{GDLZ}\) if either (i) \(\psi = \varphi \); (ii) \(\varphi \) is of the form \(\lnot \varphi '\) or \(\bigcirc \varphi '\) and \(\psi \) is a subformula of \(\varphi '\); or (iii) \(\varphi \) is of the form \(\varphi ' \wedge \varphi ''\) and \(\psi \) is a subformula of either \(\varphi '\) or \(\varphi ''\).
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Acknowledgments
Munyque Mitttelmann and Laurent Perrussel acknowledge the support of the ANR project AGAPE ANR-18-CE23-0013.
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Mittelmann, M., Perrussel, L. (2020). Game Description Logic with Integers: A GDL Numerical Extension. In: Herzig, A., Kontinen, J. (eds) Foundations of Information and Knowledge Systems. FoIKS 2020. Lecture Notes in Computer Science(), vol 12012. Springer, Cham. https://doi.org/10.1007/978-3-030-39951-1_12
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