From fibring to cryptofibring. A solution to the collapsing problem

Logica Universalis 1 (1):71-92 (2007)
.  The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For illustration, we revisit the example of combining intuitionistic and classical propositional logics.
Keywords Combining logics  fibring  the collapsing problem  cryptofibring  conservativeness
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