EXPRESSIVENESS AND DEFINABILITY IN CIRCUMSCRIPTION

• Autor(a) principal: Ferreira, Francicleber Martins
• Data de Publicação: 2015
• Outros Autores: Martins, Ana Teresa
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Manuscrito (Online)
• Texto Completo: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8642019
• topic: Minimal models. Circumscripition. Expressiveness. Definability

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 Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P; Z-minimal models of a first-order sentence is ∆- elementary, then it is elementary. That is, whenever the circumscription of a firstorder 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 ∆-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 firstorder sentence φ and whenever such class of P; Z-minimal models is ∆-elementary, then there is an explicit definition ψ for Pi such that the class of P; Z-minimal models of φ is the class of models of φ ∧ ψ. In order words, the circumscription of P in φ with Z varied can be replaced by φ plus this explicit definition ψ for Pi.