A formalisation of consistent consequence for boolean equation systems

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

1 Downloads (Pure)

Samenvatting

Boolean equation systems are sequences of least and greatest fixpoint equations interpreted over the Boolean lattice. Such equation systems arise naturally in verification problems such as the modal α-calculus model checking problem. Solving a Boolean equation system is a computationally challenging problem, and for this reason, abstraction techniques for Boolean equation systems have been developed. The notion of consistent consequence on Boolean equation systems was introduced to more effectively reason about such abstraction techniques. Prior work on consistent consequence claimed that this notion can be fully characterised by a sound and complete derivation system, building on rules for logical consequence. Our formalisation of the theory of consistent consequence and the derivation system in the proof assistant Coq reveals that the system is, nonetheless, unsound. We propose a fix for the derivation system and show that the resulting system (system CC) is indeed sound and complete for consistent consequence. Our formalisation of the consistent consequence theory furthermore points at a subtle mistake in the phrasing of its main theorem, and how to correct this.

Originele taal-2Engels
TitelInteractive theorem proving - 8th International Conference, ITP 2017,Proceedings
RedacteurenMauricio Ayala-Rincón, César A. Muñoz
UitgeverijSpringer
Pagina's462-478
Aantal pagina's17
ISBN van geprinte versie9783319661063
DOI's
StatusGepubliceerd - 2017
Evenement8th International Conference on Interactive Theorem Proving, ITP 2017 - Brasilia, Brazilië
Duur: 26 sep 201729 sep 2017

Publicatie series

NaamLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10499
ISSN van geprinte versie0302-9743
ISSN van elektronische versie1611-3349

Congres

Congres8th International Conference on Interactive Theorem Proving, ITP 2017
LandBrazilië
StadBrasilia
Periode26/09/1729/09/17

Vingerafdruk Duik in de onderzoeksthema's van 'A formalisation of consistent consequence for boolean equation systems'. Samen vormen ze een unieke vingerafdruk.

  • Citeer dit

    van Delft, M., Geuvers, H., & Willemse, T. A. C. (2017). A formalisation of consistent consequence for boolean equation systems. In M. Ayala-Rincón, & C. A. Muñoz (editors), Interactive theorem proving - 8th International Conference, ITP 2017,Proceedings (blz. 462-478). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10499). Springer. https://doi.org/10.1007/978-3-319-66107-0_29