Although quite powerful, the fibring mechanism for combining logics suffers from an anomaly usually known as "the collapsing problem". In the first accounts of fibring it could be noticed that fibring a 2-valued with a 3-valued logic would yield no fibred 3-valued models, or that the fibring of classical with intuitionistic logic would collapse into just classical logic. The source of the problem, a too strict identification of truth-values, was also the reason why the classes of models of logics being fibred were required to fulfill some closure properties. In [Sernadas,Rasga and Carnielli] modulated fibring has been introduced and shown to avoid these collapses, by means of a careful use of adjunctions between lattice structured models. In this work, we propose a structurally simpler alternative to solve the semantic collapse problem, by adopting a more general notion of fibred semantics using cryptomorphisms, in a spirit similar to the mechanisms for combining parchments in the theory of institutions. In particular, we show that the novel notion of cryptofibring encompasses the original definition of fibred model, while admiting also (initial) amalgamated models that can be used to show that the above mentioned collapses are no longer present. This talk is on ongoing joint work with A. Sernadas and C. Sernadas.
Carlos Caleiro (IST, Lisbon)
June 17, 2003