In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0,1]. We use this result to show that Esteva and Godo's logic MTL is complete with respect to interpretations into commutative residuated lattices on [0,1]. This solves an open problem raised in [3]. © 2002 Kluwer Academic Publishers.
Montagna, F., Jenei, S. (2002). A proof of standard completeness for Esteva and Godo's logic MTL. STUDIA LOGICA, 70(2), 183-192 [10.1023/A:1015122331293].
A proof of standard completeness for Esteva and Godo's logic MTL
MONTAGNA F.;
2002-01-01
Abstract
In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0,1]. We use this result to show that Esteva and Godo's logic MTL is complete with respect to interpretations into commutative residuated lattices on [0,1]. This solves an open problem raised in [3]. © 2002 Kluwer Academic Publishers.
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https://hdl.handle.net/11365/7160
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