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Weakening-free fuzzy logics with the connective \(\Updelta\)

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Abstract

This is an investigation of weakening-free fuzzy logics expanded by the delta connective \(\Updelta,\) which can be interpreted by Baaz’s projection and its generalizations. First, logical systems obtained from weakening-free uninorm (based) logics by adding \(\Updelta\) to be interpreted by the Baaz projection are introduced. Next, expansions of the weakening-free uninorm logics with \(\Updelta\) to be interpreted by its generalizations are analogously considered.

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Notes

  1. For reasons explaining the new name ‘semilinear’ in place of ‘fuzzy’ (see Cintula and Noguera 2009, 2010, 2011).

  2. We indeed have investigated such logics and their corresponding algebraic semantics on the real unit interval [0, 1], but the findings have not yet been published.

  3. For \((\Updelta_{t}),\) see Lemma 27 in Cintula (2006).

References

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Acknowledgments

I must thank the anonymous referee for his or her helpful comments and suggestions, and P. Cintula for his sending a source file for improvements in the paper.

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  1. Department of Philosophy, Chonbuk National University, Rm 213, College of Education Blvd., Jeonju, 561-756, Korea

    Eunsuk Yang

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  1. Eunsuk Yang
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Yang, E. Weakening-free fuzzy logics with the connective \(\Updelta\) . Soft Comput 16, 2089–2095 (2012). https://doi.org/10.1007/s00500-012-0879-4

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