Given a class C of t-norm BL-algebras, one may wonder which is the complexity of the set T aut (CFor All) of predicate formulas which are valid in any algebra in C. We first characterize the classes C for which T aut (CFor All) is recursively axiomatizable, and we show that this is the case iff C only consists of the Godel algebra on [0, 1]. We then prove that in all cases except from a finite number T aut (CFor All) is not even arithmetical. Finally we consider predicate monadic logics T aut(M)(CFor All) of classes C of t-norm BL-algebras, and we prove that ( possibly with finitely many exceptions) they are undecidable.
Montagna, F. (2003). On the predicate logic of continuous t-norm BL-algebras. ARCHIVE FOR MATHEMATICAL LOGIC, 44(1), 97-114 [10.1007/s00153-004-0231-5].
On the predicate logic of continuous t-norm BL-algebras
MONTAGNA F.
2003-01-01
Abstract
Given a class C of t-norm BL-algebras, one may wonder which is the complexity of the set T aut (CFor All) of predicate formulas which are valid in any algebra in C. We first characterize the classes C for which T aut (CFor All) is recursively axiomatizable, and we show that this is the case iff C only consists of the Godel algebra on [0, 1]. We then prove that in all cases except from a finite number T aut (CFor All) is not even arithmetical. Finally we consider predicate monadic logics T aut(M)(CFor All) of classes C of t-norm BL-algebras, and we prove that ( possibly with finitely many exceptions) they are undecidable.
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https://hdl.handle.net/11365/7161
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