Tableaux for free logics with descriptions
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...
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| Format: | Conference item |
| Language: | English |
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Springer
2021
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| _version_ | 1797093627220983808 |
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| author | Indrzejczak, A Zawidzki, M |
| author2 | Das, A |
| author_facet | Das, A Indrzejczak, A Zawidzki, M |
| author_sort | Indrzejczak, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:03:00Z |
| format | Conference item |
| id | oxford-uuid:c53ab040-6d7c-4126-b2e6-26b1da6cf509 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:03:00Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:c53ab040-6d7c-4126-b2e6-26b1da6cf5092022-03-27T06:29:26ZTableaux for free logics with descriptionsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c53ab040-6d7c-4126-b2e6-26b1da6cf509EnglishSymplectic ElementsSpringer2021Indrzejczak, AZawidzki, MDas, ANegri, SThe 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. |
| spellingShingle | Indrzejczak, A Zawidzki, M Tableaux for free logics with descriptions |
| title | Tableaux for free logics with descriptions |
| title_full | Tableaux for free logics with descriptions |
| title_fullStr | Tableaux for free logics with descriptions |
| title_full_unstemmed | Tableaux for free logics with descriptions |
| title_short | Tableaux for free logics with descriptions |
| title_sort | tableaux for free logics with descriptions |
| work_keys_str_mv | AT indrzejczaka tableauxforfreelogicswithdescriptions AT zawidzkim tableauxforfreelogicswithdescriptions |