Possibilistic intermediate logic

Authors:
Oscar Hernán Estrada-Estrada;José Ramón Enrique Arrazola-Ramírez;Mauricio Javier Osorio-Galindo
Affiliations:
Facultad de Cs. Físico-Matemáticas, Universidad Autónoma de Puebla, Benemérita, Av. San Claudio y Rio Verde s/n, C.P. 72560, Puebla, Mexico.;Facultad de Cs. Físico-Matemáticas, Universidad Autónoma de Puebla, Benemérita, Av. San Claudio y Rio Verde s/n, C.P. 72560, Puebla, Mexico.;Departamento de Matemáticas, Fundación Universidad de las Américas, Santa Catarina Mártir s/n, C.P. 72820, San Andrés Cholula, Puebla, México
Venue:
International Journal of Advanced Intelligence Paradigms
Year:
2012

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Abstract

We define what we call 'possibilistic intermediate logic (PIL)'; we present results analogous to those of the well-known intermediate logic, such as a deduction theorem, a generalised version of the deduction theorem, a cut rule, a weak version of a refutation theorem, a substitution theorem and Glivenko's theorem. Also, we present a definition for 'possibilistic safe beliefs'. This definition allows us to establish a relation between safe beliefs, as presented on 'applications of intuitionistic logic in answer set programming' by Osorio et al., and our version for possibilistic intermediate logic (PILX). We also present a characterisation of possibilistic safe beliefs for possibilistic normal logic programs.