TY - JOUR

T1 - Strong Decidability and Strong Recognizability

AU - Maksimova, L. L.

AU - Yun, V. F.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - Extensions of Johansson’s minimal logic J are considered. It is proved that families of negative and nontrivial logics and a series of other families are strongly decidable over J. This means that, given any finite list Rul of axiom schemes and rules of inference, we can effectively verify whether the logic with axioms and schemes, J + Rul, belongs to a given family. Strong recognizability over J is proved for known logics Neg, Gl, and KC as well as for logics LC and NC and all their extensions.

AB - Extensions of Johansson’s minimal logic J are considered. It is proved that families of negative and nontrivial logics and a series of other families are strongly decidable over J. This means that, given any finite list Rul of axiom schemes and rules of inference, we can effectively verify whether the logic with axioms and schemes, J + Rul, belongs to a given family. Strong recognizability over J is proved for known logics Neg, Gl, and KC as well as for logics LC and NC and all their extensions.

KW - admissible rule

KW - decidability

KW - Johansson algebra

KW - minimal logic

KW - recognizable logic

KW - strong decidability

UR - http://www.scopus.com/inward/record.url?scp=85035778626&partnerID=8YFLogxK

U2 - 10.1007/s10469-017-9459-0

DO - 10.1007/s10469-017-9459-0

M3 - Article

AN - SCOPUS:85035778626

VL - 56

SP - 370

EP - 385

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 5

ER -