Inverses for normal modal operators
Given a 1-ary sentence operator O, we describe L - another 1-ary operator - as a left inverse of O in a given logic if in that logic every formula φ is provably equivalent to LOφ. Similarly R is a right inverse of O if φ is always provably equivalent to ORφ. We investigate the behaviour of left and...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
1997
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| _version_ | 1826301296266706944 |
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| author | Humberstone, L Williamson, T |
| author2 | Institute of Philosophy and Sociology of the Polish Academy of Sciences |
| author_facet | Institute of Philosophy and Sociology of the Polish Academy of Sciences Humberstone, L Williamson, T |
| author_sort | Humberstone, L |
| collection | OXFORD |
| description | Given a 1-ary sentence operator O, we describe L - another 1-ary operator - as a left inverse of O in a given logic if in that logic every formula φ is provably equivalent to LOφ. Similarly R is a right inverse of O if φ is always provably equivalent to ORφ. We investigate the behaviour of left and right inverses for O taken as the □ operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right. |
| first_indexed | 2024-03-07T05:30:15Z |
| format | Journal article |
| id | oxford-uuid:e201626d-f741-44b6-ab4f-ee7d8be42b3e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:30:15Z |
| publishDate | 1997 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:e201626d-f741-44b6-ab4f-ee7d8be42b3e2022-03-27T09:58:08ZInverses for normal modal operatorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e201626d-f741-44b6-ab4f-ee7d8be42b3ePhilosophyEnglishOxford University Research Archive - ValetSpringer1997Humberstone, LWilliamson, TInstitute of Philosophy and Sociology of the Polish Academy of SciencesGiven a 1-ary sentence operator O, we describe L - another 1-ary operator - as a left inverse of O in a given logic if in that logic every formula φ is provably equivalent to LOφ. Similarly R is a right inverse of O if φ is always provably equivalent to ORφ. We investigate the behaviour of left and right inverses for O taken as the □ operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right. |
| spellingShingle | Philosophy Humberstone, L Williamson, T Inverses for normal modal operators |
| title | Inverses for normal modal operators |
| title_full | Inverses for normal modal operators |
| title_fullStr | Inverses for normal modal operators |
| title_full_unstemmed | Inverses for normal modal operators |
| title_short | Inverses for normal modal operators |
| title_sort | inverses for normal modal operators |
| topic | Philosophy |
| work_keys_str_mv | AT humberstonel inversesfornormalmodaloperators AT williamsont inversesfornormalmodaloperators |