Abstract
We present a modal language that includes explicit operators to count the number of elements that a model might include in the extension of a formula, and we discuss how this logic has been previously investigated under different guises. We show that the language is related to graded modalities and to hybrid logics. We illustrate a possible application of the language to the treatment of plural objects and queries in natural language. We investigate the expressive power of this logic via bisimulations, discuss the complexity of its satisfiability problem, define a new reasoning task that retrieves the cardinality bound of the extension of a given input formula, and provide an algorithm to solve it. © 2010 Springer-Verlag.
Cite
CITATION STYLE
Areces, C., Hoffmann, G., & Denis, A. (2010). Modal logics with counting. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6188 LNAI, pp. 98–109). https://doi.org/10.1007/978-3-642-13824-9_9
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