I study several kinds of generalisations of Montague's theorem on the method of definition of a function by recursion on a well-founded relation. In particular, I extend Montague's theorem to cover the following situations: recursion by a valuation system, non-well-founded recursion, and recursion on a dependence operator. By means of these extensions, several constructions employed in formal theories of truth and paradox can be recast as special applications of the generalised version of Montague's theorem.
Generalizing Montague’s Theorem on Recursive Definitions
Rivello, Edoardo
2021-01-01
Abstract
I study several kinds of generalisations of Montague's theorem on the method of definition of a function by recursion on a well-founded relation. In particular, I extend Montague's theorem to cover the following situations: recursion by a valuation system, non-well-founded recursion, and recursion on a dependence operator. By means of these extensions, several constructions employed in formal theories of truth and paradox can be recast as special applications of the generalised version of Montague's theorem.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
Rivello Generalising recursive definitions (Final).pdf
Accesso aperto
Tipo di file:
POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione
302.96 kB
Formato
Adobe PDF
|
302.96 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.