Fluted Logic with Counting
The fluted fragment is a fragment of first-order logic in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that the fluted fragment possesses the finite model property. In this paper, we extend the fluted fragment by the addition of counting quantifiers. We show that the resulting logic retains the finite model property, and that the satisfiability problem for its (m+1)-variable sub-fragment is in m-NExpTime for all positive m. We also consider the satisfiability and finite satisfiability problems for the extension of any of these fragments in which the fluting requirement applies only to sub-formulas having at least three free variables.
Fluted fragment
counting quantifiers
satisfiability
complexity
Theory of computation~Complexity theory and logic
141:1-141:17
Track B: Automata, Logic, Semantics, and Theory of Programming
This work was supported by the Polish NCN, grant number 2018/31/B/ST6/03662.
The author wishes to thank Prof. L. Tendera for valuable discussions.
Ian
Pratt-Hartmann
Ian Pratt-Hartmann
Department of Computer Science, University of Manchester, UK
Institute of Computer Science, University of Opole, Poland
http://www.cs.man.ac.uk/~ipratt/
https://orcid.org/0000-0003-0062-043X
10.4230/LIPIcs.ICALP.2021.141
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Ian Pratt-Hartmann
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