Modal Logics with Counting

Areces, C., Hoffmann, G., and Denis, A.. Modal Logics with Counting. In WoLLIC 2010 17th Workshop on Logic, Language, Information and Computation - WoLLIC 2010 , Brasilia, Brazil , 2010.

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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.

BibTeX: (download)

@INPROCEEDINGS{arec:moda10,
  author = {Areces, C. and Hoffmann, G. and Denis, A.},
  title = {Modal Logics with Counting},
  booktitle = {{W}o{LLIC} 2010 17th {W}orkshop on {L}ogic, {L}anguage, {I}nformation
	and {C}omputation - {W}o{LLIC} 2010 },
  year = {2010},
  address = {{B}rasilia, {B}razil },
  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.},
  keywords = {{M}odal logics ; {C}ounting}
}

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