A Mechanised Proof System for Relation Algebra Using Display Logic [chapter]

Jeremy E. Dawson, Rajeev Goré
1998 Lecture Notes in Computer Science  
We describe an implementation of the Display Logic calculus for relation algebra as an Isabelle theory. Our implementation is the rst mechanisation of any display calculus, but also provides a useful interactive proof assistant for relation algebra. The inference rules of Display Logic are coded directly as Isabelle theorems, thereby guaranteeing the correctness of all derivations. We describe various tactics and derived rules developed for simplifying proof search, including an automatic
more » ... mination procedure, and example theorems proved using Isabelle. We show how some relation algebraic theorems proved using our system can be put in the form of structural rules of Display Logic, facilitating later re-use. We then show how the implementation can be used to prove results comparing alternative formalizations of relation algebra from a proof-theoretic perspective.
doi:10.1007/3-540-49545-2_18 fatcat:hrlp65zylraxxfgi5yoomcuvki