Paper Info
Title
Is observational congruence axiomatisable in equational horn logic?
Abstract
It is well known that bisimulation on µ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either the rules are impure by involving nonequational side-conditions, or they are schematically infinitary like the congruence rule which is not Horn. It is an open question whether these complications cannot be avoided in the proof-theoretically and computationally clean and powerful setting of second-order equational Horn logic. This paper presents a positive and a negative result regarding axiomatisability of observational congruence in equational Horn logic. Firstly, we show how Milner's impure rule system can be reworked into a pure Horn axiomatisation that is complete for guarded processes. Secondly, we prove that for unguarded processes, both Milner's and Bloom/Ésik's axiomatisations are incomplete without the congruence rule, and neither system has a complete extension in rank 1 equational axioms. It remains open whether there are higher-rank equational axioms or Horn rules which would render Milner's or Bloom/Ésik's axiomatisations complete for unguarded processes.
Year
DOI
Venue
2007
10.1007/978-3-540-74407-8_14
CONCUR
Keywords
Field
DocType
equational horn logic,unguarded process,pure horn axiomatisation,equational axiom,pure equational,observational congruence axiomatisable,equational logic,higher-rank equational axiom,congruence rule,horn logic,horn rule
Discrete mathematics,Axiom,Horn logic,Bisimulation,Equational logic,Process calculus,Congruence (geometry),Mathematics
Conference
Volume
ISSN
ISBN
4703
0302-9743
3-540-74406-1
Citations 
PageRank 
References 
1
0.34
22
Authors
2
Name
Order
Citations
PageRank
Michael Mendler131434.60
Gerald Lüttgen260040.71