TY - CHAP
T1 - Rewriting with linear inferences in propositional logic
AU - Das, A.
PY - 2013/6/14
Y1 - 2013/6/14
N2 - Linear inferences are sound implications of propositional logic where each variable appears exactly once in the premiss and conclusion. We consider a specific set of these inferences, MS, first studied by Straßburger, corresponding to the logical rules in deep inference proof theory. Despite previous results characterising the individual rules of MS, we show that there is no polynomialtime characterisation of MS, assuming that integers cannot be factorised in polynomial time. We also examine the length of rewrite paths in an extended system MSU that also has unit equations, utilising a notion dubbed trivialisation to reduce the case with units to the case without, amongst other observations on MS-rewriting and the set of linear inferences in general.
AB - Linear inferences are sound implications of propositional logic where each variable appears exactly once in the premiss and conclusion. We consider a specific set of these inferences, MS, first studied by Straßburger, corresponding to the logical rules in deep inference proof theory. Despite previous results characterising the individual rules of MS, we show that there is no polynomialtime characterisation of MS, assuming that integers cannot be factorised in polynomial time. We also examine the length of rewrite paths in an extended system MSU that also has unit equations, utilising a notion dubbed trivialisation to reduce the case with units to the case without, amongst other observations on MS-rewriting and the set of linear inferences in general.
UR - http://www.scopus.com/inward/record.url?scp=84889597863&partnerID=8YFLogxK
UR - http://dx.doi.org/10.4230/LIPIcs.RTA.2013.158
U2 - 10.4230/LIPIcs.RTA.2013.158
DO - 10.4230/LIPIcs.RTA.2013.158
M3 - Chapter or section
AN - SCOPUS:84889597863
SN - 9783939897538
VL - 21
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 158
EP - 173
BT - 24th International Conference on Rewriting Techniques and Applications (RTA 2013)
A2 - van Raamsdonk, F.
PB - Leibniz International Proceedings in Informatics
CY - Dagstuhl, Germany
ER -