# A Mechanised Proof System for Relation Algebra using Display Logic

@inproceedings{Dawson1998AMP, title={A Mechanised Proof System for Relation Algebra using Display Logic}, author={Jeremy E. Dawson and Rajeev Gor{\'e}}, booktitle={JELIA}, year={1998} }

We describe an implementation of the Display Logic calculus for relation algebra as an Isabelle theory. Our implementation is the first mechanisation of any display calculus. The inference rules of Display Logic are coded directly as Isabelle theorems, thereby guaranteeing the correctness of all derivations. Our implementation generalises easily to handle other display calculi. It also provides a useful interactive proof assistant for relation algebras.
We describe various tactics and…

## 13 Citations

### Embedding Display Calculi into Logical Frameworks: Comparing Twelf and Isabelle

- Computer ScienceCATS
- 2001

### System Description: ARA - An Automatic Theorem Prover for Relation Algebras

- MathematicsCADE
- 2000

aRa, the implementation in Haskell, offers different reduction strategies for RPC n, and a set of simplifications preserving n-variable provability, and can prove validity in the theories of simple semi-associative relation algebras, relation alagbras and representable relation alGEbras.

### Machine-checked Cut-elimination for Display Logic

- Computer Science
- 2006

A new proof of cut-elimination for all display calculi which does not reply on the usual double induction on the grade and weight of a cut is presented.

### A Mechanisation of Classical Modal Tense Logics Using Isabelle

- Computer ScienceAustralian Joint Conference on Artificial Intelligence
- 1998

This work presents an implementation of an interactive theorem prover for the basic tense logic K t, and many of its extensions, using the generic proof assistant Isabelle, using a Display Logic formalism of K t as opposed to a traditional Gentzen system.

### Display Calculi for Nominal Tense Logics

- MathematicsJ. Log. Comput.
- 2002

It is shown that every -valid formula admits a cut-free derivation in Æ and that a restricted display calculus Æ, is not only complete for , but that it enjoys cut-elimination for arbitrary sequents.

### Display Calculi for Logics with Relative Accessibility Relations

- Computer Science, PhilosophyJ. Log. Lang. Inf.
- 2000

This work translates the knowledgelogics into polymodal logics axiomatised by primitive axioms and uses Kracht's results on properly displayable logics to define cut-free display calculi for knowledge logics.

### Substructural Logics on Display

- Philosophy, Computer ScienceLog. J. IGPL
- 1998

A single (cut-free) Display calculus for the Bi-Lambek Calculus, from which all the well-known (bi-intuitionistic and bi-classical) extensions are obtained by the incremental addition of structural rules to a constant core of logical introduction rules.

### Two Proof Systems for Peirce Algebras

- MathematicsRelMiCS
- 2003

Two tableaux-style proof systems for Peirce algebras are developed and compared, one is a tableau refutation proof system, the other is a proof system in the style of Rasiowa-Sikorski.

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