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 ...

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 ...

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 ...