Basic infobase change (Q5943016)

The paper is very similar to the paper of \textit{T. A. Meyer, W. A. Labuschagne}, and \textit{J. Heidema}: ``Infobase change: A first approximation'' [J. Logic, Lang. Inf. 9, 353-377 (2000; Zbl 0964.03016)], here referred to as Meyer et al. That is, an approach to infobase change is presented for which the associated theory change operations satisfy all the AGM postulates. These operations determine which wffs in the infobase should be retained after an infobase change. The wffs that cannot be retained are not simply discarded, but are weakened in an appropriate fashion. A form of belief change that attempts to retain the advantages of theory change as well as base change while simultaneously discarding the disadvantages of both is proposed. This proposal is an extension of the work of Meyer et al. in two ways. Firstly, an infobase is viewed as a finite sequence of wffs (not as a set of wffs, as has been done in Meyer et al.). This enables us to keep an intuition of independently obtained pieces of information in each wff. Secondly, the approach of Meyer et al. associates a unique infobase contraction and revision operation with every infobase. This approach is generalized here by allowing for a whole spectrum of infobase contraction and revision operations, ranging from a ``foundational'' approach (only the set of discarded wffs themselves is involved in the construction of their weakened versions), at the one extreme, to a ``coherentist'' approach (all the wffs in an infobase play a role in determining the weakened versions of the discarded wffs), at the other. The fact that iterated infobase change, as defined in this paper, satisfies the DP-postulates, unlike the initial version in Meyer et al. serves as a confirmation that the current proposal is a step in the right direction.