Periodicity and Reflexivity in Revision Sequences
Abstract Revision sequences were introduced in 1982 by Herzberger and Gupta (independently) as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Rivello, Edoardo [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Systematik: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Studia logica - Springer Netherlands, 1953, 103(2015), 6 vom: 11. Juni, Seite 1279-1302 |
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| Übergeordnetes Werk: |
volume:103 ; year:2015 ; number:6 ; day:11 ; month:06 ; pages:1279-1302 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11225-015-9619-y |
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OLC2033923428 |
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| 520 | |a Abstract Revision sequences were introduced in 1982 by Herzberger and Gupta (independently) as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so-called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis. | ||
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10.1007/s11225-015-9619-y doi (DE-627)OLC2033923428 (DE-He213)s11225-015-9619-y-p DE-627 ger DE-627 rakwb eng 000 100 VZ 5,1 17,1 ssgn PHILOS DE-12 fid LING DE-30 fid SA 8098 VZ rvk SA 8098 VZ rvk SA 8098 CA 1000 VZ rvk Rivello, Edoardo verfasserin (orcid)0000-0003-2642-9270 aut Periodicity and Reflexivity in Revision Sequences 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2015 Abstract Revision sequences were introduced in 1982 by Herzberger and Gupta (independently) as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so-called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis. Revision theory of truth Revision sequences Transfinite sequences Enthalten in Studia logica Springer Netherlands, 1953 103(2015), 6 vom: 11. Juni, Seite 1279-1302 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:103 year:2015 number:6 day:11 month:06 pages:1279-1302 https://doi.org/10.1007/s11225-015-9619-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_2088 GBV_ILN_4035 GBV_ILN_4193 SA 8098 SA 8098 SA 8098 AR 103 2015 6 11 06 1279-1302 |
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Periodicity and Reflexivity in Revision Sequences |
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Periodicity and Reflexivity in Revision Sequences |
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periodicity and reflexivity in revision sequences |
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Periodicity and Reflexivity in Revision Sequences |
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Abstract Revision sequences were introduced in 1982 by Herzberger and Gupta (independently) as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so-called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis. © Springer Science+Business Media Dordrecht 2015 |
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Abstract Revision sequences were introduced in 1982 by Herzberger and Gupta (independently) as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so-called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis. © Springer Science+Business Media Dordrecht 2015 |
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Abstract Revision sequences were introduced in 1982 by Herzberger and Gupta (independently) as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so-called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis. © Springer Science+Business Media Dordrecht 2015 |
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