A Type-Directed Negation Elimination

Etienne Lozes
(ENS Cachan, CNRS)

In the modal mu-calculus, a formula is well-formed if each recursive variable occurs underneath an even number of negations. By means of De Morgan's laws, it is easy to transform any well-formed formula into an equivalent formula without negations – its negation normal form. Moreover, if the formula is of size n, its negation normal form of is of the same size O(n). The full modal mu-calculus and the negation normal form fragment are thus equally expressive and concise.

In this paper we extend this result to the higher-order modal fixed point logic (HFL), an extension of the modal mu-calculus with higher-order recursive predicate transformers. We present a procedure that converts a formula into an equivalent formula without negations of quadratic size in the worst case and of linear size when the number of variables of the formula is fixed.

In Ralph Matthes and Matteo Mio: Proceedings Tenth International Workshop on Fixed Points in Computer Science (FICS 2015), Berlin, Germany, September 11-12, 2015, Electronic Proceedings in Theoretical Computer Science 191, pp. 132–142.
Published: 9th September 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.191.12 bibtex PDF
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