The Fixed Point Property in Modal Logic
This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every n\geq 2, K+\square(\square^{...
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| Veröffentlicht in: | Notre Dame journal of formal logic 2001, Vol.42 (2), p.65-86 |
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| container_title | Notre Dame journal of formal logic |
| container_volume | 42 |
| creator | Sacchetti, Lorenzo |
| description | This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every
n\geq 2, K+\square(\square^{n-1}p\rightarrow p)\rightarrow\square p has the explicit
fixed point property. Our main result states that every complete modal logic
L having the Craig's interpolation property and such that
L\vdash\Delta(\nabla(p)\rightarrow p)\rightarrow\Delta(p) , where \nabla(p) and \Delta(p)
are suitable modal formulas, has the explicit fixed point property. |
| doi_str_mv | 10.1305/ndjfl/1054837934 |
| format | Article |
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n\geq 2, K+\square(\square^{n-1}p\rightarrow p)\rightarrow\square p has the explicit
fixed point property. Our main result states that every complete modal logic
L having the Craig's interpolation property and such that
L\vdash\Delta(\nabla(p)\rightarrow p)\rightarrow\Delta(p) , where \nabla(p) and \Delta(p)
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n\geq 2, K+\square(\square^{n-1}p\rightarrow p)\rightarrow\square p has the explicit
fixed point property. Our main result states that every complete modal logic
L having the Craig's interpolation property and such that
L\vdash\Delta(\nabla(p)\rightarrow p)\rightarrow\Delta(p) , where \nabla(p) and \Delta(p)
are suitable modal formulas, has the explicit fixed point property.</description><subject>03B45</subject><subject>03F30</subject><subject>03F40</subject><subject>03F45</subject><subject>fixed points</subject><subject>modal logic</subject><subject>provability predicates</subject><issn>0029-4527</issn><issn>1939-0726</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNplkM9LwzAYhoMoWKd3j715qvu-pGmaoxY3hYo7bOeS5Ydm1KakFdx_73RFD55eeOF54H0JuUa4RQZ83pmda-cIPC-ZkCw_IQlKJjMQtDglCQCVWc6pOCcXw7ADwJzLPCE36zebLvynNekq-G5MVzH0No771HfpczCqTevw6vUlOXOqHezVlDOyWTysq8esflk-VXd1punBl9ktKMPKHAuNWHCQDg2CVdzKLVOCowbLmdClcg4kpxSVAyMkd45LWzA2I_dHbx_DzurRfujWm6aP_l3FfROUb6pNPbVT_Exv_qYfJHCU6BiGIVr3yyM032_9R74ABNpdaA</recordid><startdate>2001</startdate><enddate>2001</enddate><creator>Sacchetti, Lorenzo</creator><general>Duke University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2001</creationdate><title>The Fixed Point Property in Modal Logic</title><author>Sacchetti, Lorenzo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2594-eb0ad38416c116509f1d10ea5e9b3a751c0e537c8aff095221af0d795ff59e633</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>03B45</topic><topic>03F30</topic><topic>03F40</topic><topic>03F45</topic><topic>fixed points</topic><topic>modal logic</topic><topic>provability predicates</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sacchetti, Lorenzo</creatorcontrib><collection>CrossRef</collection><jtitle>Notre Dame journal of formal logic</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sacchetti, Lorenzo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Fixed Point Property in Modal Logic</atitle><jtitle>Notre Dame journal of formal logic</jtitle><date>2001</date><risdate>2001</risdate><volume>42</volume><issue>2</issue><spage>65</spage><epage>86</epage><pages>65-86</pages><issn>0029-4527</issn><eissn>1939-0726</eissn><abstract>This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every
n\geq 2, K+\square(\square^{n-1}p\rightarrow p)\rightarrow\square p has the explicit
fixed point property. Our main result states that every complete modal logic
L having the Craig's interpolation property and such that
L\vdash\Delta(\nabla(p)\rightarrow p)\rightarrow\Delta(p) , where \nabla(p) and \Delta(p)
are suitable modal formulas, has the explicit fixed point property.</abstract><pub>Duke University Press</pub><doi>10.1305/ndjfl/1054837934</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0029-4527 |
| ispartof | Notre Dame journal of formal logic, 2001, Vol.42 (2), p.65-86 |
| issn | 0029-4527 1939-0726 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_ndjfl_1054837934 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete |
| subjects | 03B45 03F30 03F40 03F45 fixed points modal logic provability predicates |
| title | The Fixed Point Property in Modal Logic |
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