Some articles on mtl, algebras:
Monoidal T-norm Logic - Semantics - General Semantics - General Soundness and Completeness Theorems
... The logic MTL is sound and complete with respect to the class of all MTL-algebras (Esteva Godo, 2001) A formula is provable in MTL if and only if it is valid in all MTL-algebras ... The notion of MTL-algebra is in fact so defined that MTL-algebras form the class of all algebras for which the logic MTL is sound ... A formula A is a global consequence in MTL of a set of formulae Γ if and only if A is derivable from Γ in MTL ...
... The logic MTL is sound and complete with respect to the class of all MTL-algebras (Esteva Godo, 2001) A formula is provable in MTL if and only if it is valid in all MTL-algebras ... The notion of MTL-algebra is in fact so defined that MTL-algebras form the class of all algebras for which the logic MTL is sound ... A formula A is a global consequence in MTL of a set of formulae Γ if and only if A is derivable from Γ in MTL ...
Monoidal T-norm Logic - Semantics - Linear Semantics
... Like algebras for other fuzzy logics, MTL-algebras enjoy the following linear subdirect decomposition property Every MTL-algebra is a subdirect product of linearly ordered MTL-algebras ... An MTL-algebra is linearly ordered if its lattice order is linear.) In consequence of the linear subdirect decomposition property of all MTL-algebras, the completeness theorem with respect to linear MTL-algebras ... A formula A is derivable in MTL from a set of formulae Γ if and only if A is a global consequence in all linear MTL-algebras of Γ ...
... Like algebras for other fuzzy logics, MTL-algebras enjoy the following linear subdirect decomposition property Every MTL-algebra is a subdirect product of linearly ordered MTL-algebras ... An MTL-algebra is linearly ordered if its lattice order is linear.) In consequence of the linear subdirect decomposition property of all MTL-algebras, the completeness theorem with respect to linear MTL-algebras ... A formula A is derivable in MTL from a set of formulae Γ if and only if A is a global consequence in all linear MTL-algebras of Γ ...
Monoidal T-norm Logic - Semantics
... logics, algebraic semantics is predominantly used for MTL, with three main classes of algebras with respect to which the logic is complete General semantics, formed of all MTL-algebras — that is, all algebras for ...
... logics, algebraic semantics is predominantly used for MTL, with three main classes of algebras with respect to which the logic is complete General semantics, formed of all MTL-algebras — that is, all algebras for ...
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