Title: Possibilistic intermediate logic

Authors: Oscar Hernán Estrada-Estrada; José Ramón Enrique Arrazola-Ramírez; Mauricio Javier Osorio-Galindo

Addresses: 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

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.

Keywords: possibilistic logic; intermediate logic; answer sets; safe beliefs; uncertainty; uncertain information.

DOI: 10.1504/IJAIP.2012.048143

International Journal of Advanced Intelligence Paradigms, 2012 Vol.4 No.2, pp.149 - 167

Published online: 23 Aug 2014 *

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