# Cut-free Display Calculi for Relation Algebras

@inproceedings{Gor1996CutfreeDC, title={Cut-free Display Calculi for Relation Algebras}, author={Rajeev Gor{\'e}}, booktitle={CSL}, year={1996} }

We extend Belnap's Display Logic to give a cut-free Gentzen-style calculus for relation algebras. The calculus gives many axiomatic extensions of relation algebras by the addition of further structural rules. It also appears to be the first purely prepositional Gentzen-style calculus for relation algebras.

## 24 Citations

### 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.

### Formalised Cut Admissibility for Display Logic

- Mathematics, Computer ScienceTPHOLs
- 2002

This work uses a deep embedding of the display calculus for relation algebras δRA in the logical framework Isabelle/HOL to formalise a machine-checked proof of cut-admissibility for δ RA and believes this to be the first full formalisation of Cut-Admissibility in the presence of explicit structural rules.

### Theoremhood Preserving Maps as a Characterisation of Cut Elimination for Provability Logics

- Mathematics
- 1999

We deene cut-free display calculi for provability (modal) logics that are not properly displayable according to Kracht's analysis. We also show that a weak form of the cut-elimination theorem (for…

### Dual Intuitionistic Logic Revisited

- Computer ScienceTABLEAUX
- 2000

It is shown that a previously reported generalised display framework does deliver the required cut-free display calculus and the structural rule necessary to turn this display calculus into one for classical logic is pinpointed.

### TABLEAUX 2005 Position Papers and Tutorial Descriptions

- Philosophy
- 2005

We present tableaux calculi for some logics of default reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableaux proof procedure for preferential logic P and for loop-cumulative logic…

### A Mechanised Proof System for Relation Algebra using Display Logic

- Computer Science, MathematicsJELIA
- 1998

This work describes an implementation of the Display Logic calculus for relation algebra as an Isabelle theory, and shows how some relation algebraic theorems proved using this system can be put in the form of structural rules of Display Logic, facilitating later re-use.

### 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.

### Predicate Logics on Display

- Philosophy, Computer ScienceStud Logica
- 1999

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal…

### Algebraic Models and Complete Proof Calculi for Classical BI

- Computer Science, Mathematics
- 2008

A class of algebraic models for CBI is presented which permit the full range of classical multiplicative connectives to be modelled, and can be seen as generalisations of Abelian groups.

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