Subject: Paper announcement: CMDL in CoS
Newsgroups: gmane.science.mathematics.frogs
Date: 2006-09-12 01:01:11 GMT (1 year, 34 weeks, 4 days, 21 hours and 7 minutes ago)
Hi, Rajeev Gore and I recently wrote a paper on relating display logics and the calculus of structures. We did a case study on encoding classical modal display logic (CMDL) of Wansing into CoS. Through primitive extensions of CMDL, we managed to get a minimal cut free CoS system for S5. Details of the paper is given below, including a link to a draft. Comments and suggestions are most welcome. -Alwen -- Classical Modal Display Logic in the Calculus of Structures and Minimal and Cut-free Deep Inference Calculi for S5 by Rajeev Gore and Alwen Tiu. Abstract: We begin by showing how to faithfully encode the Classical Modal Display Logic (CMDL) of Wansing into the Calculus Of Structures (CoS) of Guglielmi. Since every CMDL calculus enjoys cut-elimination, we obtain a cut-elimination theorem for all corresponding CoS calculi. We then show how our result leads to a minimal cut-free CoS calculus for modal logic $\SFive$. As far as we know, no other existing CoS calculi for $\SFive$ enjoy both these properties simultaneously. Link: http://users.rsise.anu.edu.au/~tiu/papers/cmdl.pdf