%0 Journal Article
%T Expressiveness and definability in circumscription
%A Ferreira
%A Francicleber Martins
%A Martins
%A Ana Teresa
%J Manuscrito
%D 2011
%I Universidade Estadual de Campinas
%R 10.1590/S0100-60452011000100011
%X we investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of circumscription. first, we give a proof of the failure of the l£¿wenheim-skolem theorem for circumscription. then we show that, if the class of p; z-minimal models of a first-order sentence is ¦Ä-elementary, then it is elementary. that is, whenever the circumscription of a first-order sentence is equivalent to a first-order theory, then it is equivalent to a finitely axiomatizable one. this means that classes of models of circumscribed theories are either elementary or not ¦Ä-elementary. finally, using the previous result, we prove that, whenever a relation pi is defined in the class of p; z-minimal models of a first-order sentence ¦Õ and whenever such class of p; z-minimal models is ¦Ä-elementary, then there is an explicit definition ¦× for pi such that the class of p; z-minimal models of ¦Õ is the class of models of ¦Õ ¡Ä ¦×. in order words, the circumscription of p in ¦Õ with z varied can be replaced by ¦Õ plus this explicit definition ¦× for pi.
%K minimal models
%K circumscripition
%K expressiveness
%K definability.
%U http://www.scielo.br/scielo.php?script=sci_abstract&pid=S0100-60452011000100011&lng=en&nrm=iso&tlng=en