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 recurrent hypothesis and draw from this fact some observations about the problem of chosing the "right” limit rule when performing a revision-theoretic analysis.

Periodicity and reflexivity in revision sequences

Rivello E
2015-01-01

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 recurrent hypothesis and draw from this fact some observations about the problem of chosing the "right” limit rule when performing a revision-theoretic analysis.
2015
103
6
1279
1302
https://link.springer.com/article/10.1007/s11225-015-9619-y
Revision theory of truth; Revision sequences
Rivello E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1762869
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