A Type-Directed Negation Elimination
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2015-09-01
|
| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1509.03020v1 |
| _version_ | 1811320951449583616 |
|---|---|
| author | Etienne Lozes |
| author_facet | Etienne Lozes |
| author_sort | Etienne Lozes |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T13:08:26Z |
| format | Article |
| id | doaj.art-8818e2d534aa4de3ba13cbbddd9b5e57 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-04-13T13:08:26Z |
| publishDate | 2015-09-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-8818e2d534aa4de3ba13cbbddd9b5e572022-12-22T02:45:41ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802015-09-01191Proc. FICS 201513214210.4204/EPTCS.191.12:1A Type-Directed Negation EliminationEtienne Lozes0 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.http://arxiv.org/pdf/1509.03020v1 |
| spellingShingle | Etienne Lozes A Type-Directed Negation Elimination Electronic Proceedings in Theoretical Computer Science |
| title | A Type-Directed Negation Elimination |
| title_full | A Type-Directed Negation Elimination |
| title_fullStr | A Type-Directed Negation Elimination |
| title_full_unstemmed | A Type-Directed Negation Elimination |
| title_short | A Type-Directed Negation Elimination |
| title_sort | type directed negation elimination |
| url | http://arxiv.org/pdf/1509.03020v1 |
| work_keys_str_mv | AT etiennelozes atypedirectednegationelimination AT etiennelozes typedirectednegationelimination |