Modal Logics with Counting

Carlos Areces (1) , Guillaume Hoffmann (1) , Alexandre A. J. Denis (1)

1 TALARIS - Natural Language Processing: representation, inference and semantics

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.

Mots clés: Modal logics; Counting

Domaines: Logique [math.LO]; Interface homme-machine [cs.HC]

Carlos Areces, Guillaume Hoffmann, Alexandre A. J. Denis. Modal Logics with Counting. 17th Workshop on Logic, Language, Information and Computation - WoLLIC 2010, Jul 2010, Brasilia, Brazil. ⟨hal-00482337⟩