Tableaux for free logics with descriptions

Conference item

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 NQFL− 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.

Authors: Indrzejczak, A; Zawidzki, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Host title: Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2021
• Pages: 56-73
• Series: Lecture Notes in Computer Science
• Publication date: 2021-08-30
• Acceptance date: 2021-06-14
• Event title: 30th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2021)
• Event location: Birmingham, UK
• Event website: https://tableaux2021.org/
• Event start date: 2021-09-06
• Event end date: 2021-09-09
• DOI: 10.1007/978-3-030-86059-2_4
• ISSN: 0302-9743
• EISBN: 978-3-030-86059-2
• ISBN: 978-3-030-86058-5
• Language: English
• Keywords: FFR; free logics; analytic tableaux; definite descriptions