an:06234676
Zbl 1323.03029
Odintsov, Sergei; Rybakov, Vladimir
Unification and admissible rules for paraconsistent minimal Johanssons' logic J and positive intuitionistic logic \(\mathbf{IPC}^+\)
EN
Ann. Pure Appl. Logic 164, No. 7-8, 771-784 (2013).
00327017
2013
j
03B53 03B25 68T15
paraconsistent minimal Johanssons' logic; positive intuitionistic logic; admissible inference rules; unifiers; unification problem
Summary: We study unification problem and problem of admissibility for inference rules in minimal Johanssons' logic J and positive intuitionistic logic \(\mathrm{IPC}^+\). This paper proves that the problem of admissibility for inference rules with coefficients (parameters) (as well as plain ones -- without parameters) is decidable for the paraconsistent minimal Johanssons' logic J and the positive intuitionistic logic \(\mathrm{IPC}^+\). Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability of formulas with coefficients also works via verification of admissibility.