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Non-Classical Logics. Theory and Applications (NCL) is an international conference aimed at presenting novel results and survey works in widely understood non-classical logics and their applications. This year's edition was also an opportunity to celebrate the 50th anniversary of the logic journal Bulletin of the Section of Logic (BSL), established in 1971 and since then published by the University of Lodz. On this occassion a number of renowned researchers having bonds with BSL were asked to deliver invited talks. Additionally, during the conference a special session was held commemorating J. Michael Dunn, outstanding logician and collecting editor of BSL, who passed away in 2021. Finally, collocated with the conference were three workshops devoted to, subsequently, non-Fregean logics, relating logics, and formal ontology, as well as a tutorial on graded logic.

The paper provides a tableau approach to definite descriptions. We focus on several formalizations of the so-called minimal free description theory (MFD) usually formulated axiomatically in the setting of free logic. We consider five analytic tableau systems corresponding to different kinds of free logic, including the logic of definedness applied in computer science and constructive mathematics for dealing with partial functions (here called negative quasi-free logic). The tableau systems formalise MFD based on PFL (positive free logic), NFL (negative free logic), PQFL and NQFL (the quasi-free counterparts of the former ones). Also the logic NQFLm is taken into account, which is equivalent to NQFL, but whose language does not comprise the existence predicate. It is shown that all tableaux are sound and complete with respect to the semantics of these logics., Comment: This is a full version of a conference paper that will appear in the proceedings of the 30th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX)