In this work we investigate several complexity and definability problems for the logic L Pi 1/2. We show that the universal fragment of the theory of real closed fields can be faithfully interpreted in such a logic. Then we investigate the logics of t-norms definable in L Pi 1/2 and we prove that they are all in PSPACE. Finally we show that the most important fuzzy logics are complete with respect to classes of t-norms which are definable in L Pi 1/2.
Montagna, F., Marchioni, E. (2007). Complexity and definability issues in ŁΠ½. JOURNAL OF LOGIC AND COMPUTATION, 17(2), 311-331 [10.1093/logcom/exl044].
Complexity and definability issues in ŁΠ½
MONTAGNA, FRANCO;
2007-01-01
Abstract
In this work we investigate several complexity and definability problems for the logic L Pi 1/2. We show that the universal fragment of the theory of real closed fields can be faithfully interpreted in such a logic. Then we investigate the logics of t-norms definable in L Pi 1/2 and we prove that they are all in PSPACE. Finally we show that the most important fuzzy logics are complete with respect to classes of t-norms which are definable in L Pi 1/2.
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https://hdl.handle.net/11365/7166
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