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In (Jenei and Montagna, 2003) was proved that the non-commutative psMTL logic introduced in (Hájek, 2003b) is the logic of left-continuous non-commutative t-norms or, equivalently, that the logic psMTL enjoys standard completeness. In the present paper we provide an alternative proof for the standard completeness theorem for the logic psMTL and we furthermore show that this result can be obtained also for finite theories.

Non-commutative Fuzzy Logic psMTL - An Alternative Proof for the Standard Completeness Theorem