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05502963 {\L}ukowski, Piotr The procedures for belief revision. Makinson, David (ed.) et al., Towards mathematical philosophy. Papers from the Studia Logica conference Trends in Logic IV, Toru\'n, Poland, September 1--4, 2006. Berlin: Springer (ISBN 978-1-4020-9083-7/hbk; 978-1-4020-9084-4/e-book). Trends in Logic--Studia Logica Library 28, 249-268 (2009). 2009 Berlin: Springer EN consequence operations dual consequence operations elimination operations contraction revision logic of truth logic of falsehood nonmonotonic reasoning classical logic Heyting-Brouwer logic intuitionistic logic

doi:10.1007/978-1-4020-9084-4_13

In a paper of 1973, Ryszard W\'ojcicki introduced the notion of the dual of a consequence operation. As is well known, if $V$ is a set of valuations on a propositional language into $\{0,1\}$, we may use it to define a consequence operation $Cn$ by the rule: put $y$ in $Cn(X)$ iff for no $v$ in $V$ do we have $v(y) = 0$ while $v(x) = 1$ for all $x$ in $X$. W\'ojcicki defined the dual operation $Cd$ by inverting 0 and 1 in the above. In a paper of 2002, Lukowski used this to define the elimination-counterpart $E$ of such a consequence operation $Cn$: put $y$ in $E(X)$ iff it is not in $Cd(L\setminus X)$, i.e. iff for some valuation $v$ in $V$ we have $v(y) = 1$ while $v(z) = 0$ for all $z$ outside $X$. Since immediately we get $E(X)$ to be a subset of $X$, one may wonder whether it may in turn be used to define functions akin to the contraction operations of AGM belief change theory. In the paper under review, the author proposes such a definition and examines the behaviour of the resulting contraction-like operations as well as the induced revision-like ones. He also considers the same in a non-classical context, where the initial consequence operation $Cn$ is not the classical one but rather a certain augmented intuitionistic logic introduced by Rauszer in 1974. David Makinson (London)