Abstract.
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.
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Mathematics Subject Classification (2000): 03B22 (03B35, 03G25, 03G30)
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Caleiro, C., Ramos, J. From Fibring to Cryptofibring. A Solution to the Collapsing Problem. Log. univers. 1, 71–92 (2007). https://doi.org/10.1007/s11787-006-0004-5
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DOI: https://doi.org/10.1007/s11787-006-0004-5