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On two fragments with negation and without implication of the logic of residuated lattices
2005
Archive for Mathematical Logic
The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called FL ew by Ono), etc. In this paper we study the ∨, * , ¬, 0, 1 -fragment and the ∨, ∧, * , ¬, 0, 1 -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment
doi:10.1007/s00153-005-0324-9
fatcat:a3sqyaylw5gmdmhdv5ocalzmtm