Technical Report TR-ARP-12-95

Automated Reasoning Project
Research School of Information Sciences and Engineering
and Centre for Information Science Research
Australian National University

June, 1995

Solving the Display Problem via Residuation

Rajeev Gor?e

Abstract The display problem" of Belnap is an attempt to compare and contrast the P-scheme of Belnap and the A-scheme of Wansing, each of which have the display property. Restall has recenly shown that relevant logics can be better displayed using a third scheme. We show that the C-scheme presented here is a generalisation of all of these schemes by showing how to obtain each of the other schemes, plus other related cousins, all from the C-scheme. We then give a systematic method for obtaining other schemes, all based on the algebraic notions of Galois connections, residuation, and their duals. We thus begin the task of explicitly connecting Belnap's Display Logic and Dunn's Gaggle Theory.