From Fibring to Cryptofibring. A Solution to the Collapsing Problem |
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Authors: | Carlos Caleiro Jaime Ramos |
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Affiliation: | (1) SQIG-IT and CLC, Department of Mathematics, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
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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. Mathematics Subject Classification (2000): 03B22 (03B35, 03G25, 03G30) |
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Keywords: | KeywordHeading" >. Combining logics fibring the collapsing problem cryptofibring conservativeness |
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