Olá, Valeria: Acho que vale a pena recordar ainda que há uma outra maneira bastante simples de "consertar" os formalismos dedutivos modais, pelo acréscimo de etiquetas (representando termos de uma assinatura de primeira ordem adequada) sobre fórmulas modais e a adição de fórmulas relacionais à linguagem-objeto. Como resultado, regras de dedução natural extremamente simples para os principais sistemas modais podem ser definidas, tal como ilustradas no livro "Labelled Non-Classical Logics", de Luca Viganò --- ou no seguinte material nosso, em português: http://www.dimap.ufrn.br/~jmarcos/courses/LC/Cap4.pdf
As lógicas híbridas, claro, vão muito além disso, sendo baseadas em linguagens legitimamente *mais expressivas* do ponto de vista das estruturas relacionais por elas caracterizadas, como Mário bem chamou a atenção em sua mensagem. Abraços, Joao Marcos On Sat, May 19, 2012 at 1:01 PM, Valeria de Paiva <valeria.depa...@gmail.com> wrote: > Tony, > as far as I'm concerned the real advantage of hybrid logics over multimodal > logics is on their proof theoretical aspects, hybrid logics are much better > behaved than modal logics as far as their proof theory goes. Patrick > Blackburn gave a course in nasslli2002 where he pressed this point and i've > spent an enjoyable half an hour trying to find the slides to send you, but > have not. the reader for the course is available > www.stanford.edu/group/nasslli/courses/*blackburn*/reader.pdf. > > in particular interpolation results are recovered: > (Repairing the Interpolation Theorem in Quantified Modal > Logic<http://www.loria.fr/%7Eblackbur/papers/repairing.pdf>, > by Carlos Areces, Patrick Blackburn and Maarten Marx. *Annals of Pure and > Applied Logic*, 124, 287-299, 2003. ) > > but for me the big payoff was on cut-elimination results for several > systems. > > Patrick's lectures were impressive enough to make me investigate > constructive versions of hybrid logics with Torben Brauner to begin with > and more recently with Herman Hauesler and Alexandre Rademaker. > > and yes, satisfaction operators do behave like modal operators. > > but no, it's not simply giving new names to old things, since using the > satisfaction operators and internalizing the models as part of your syntax > you genuinely get a different logic system, which has different inferential > properties and which you can implement and do more things with. > at least this is my take. > > []s, > Valeria -- http://sequiturquodlibet.googlepages.com/ _______________________________________________ Logica-l mailing list Logica-l@dimap.ufrn.br http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
