Independence friendly logic with classical negation via flattening is a second-order logic with weak dependencies

• Autores: Figueira, Santiago; Gorin, Daniel Alejadro; Grimson, Rafael
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Independence Friendly Logic; Second Order Logic; Henkin Quantifiers; Classical Negation
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

It is well-known that Independence Friendly (IF) logic is equivalent to existential secondorder logic (Σ1 1 ) and, therefore, is not closed under classical negation. The Boolean closure of IF sentences, called Extended IF-logic, on the other hand, corresponds to a proper fragment of 1 2. In this article we consider SL(↓), IF-logic extended with Hodges’ flattening operator ↓, which allows to define a classical negation. SL(↓) contains Extended IF-logic and hence it is at least as expressive as the Boolean closure of Σ1 1 . We prove that SL(↓) corresponds to a weak syntactic fragment of SO which we show to be strictly contained in 1 2. The separation is derived almost trivially from the fact that Σ1 n defines its own truth-predicate. We finally show that SL(↓) is equivalent to the logic of Henkin quantifiers, which shows, we argue, that Hodges’ notion of negation is adequate.
Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Gorin, Daniel Alejadro. Friedrich Alexander Universität Erlangen-Nürnberg. Department of Computer Science; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Grimson, Rafael. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina