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THE EXPRESSIVE POWER OF MEMORY LOGICS

Published online by Cambridge University Press:  08 June 2011

CARLOS ARECES*
Affiliation:
INRIA Nancy Grand Est
DIEGO FIGUEIRA*
Affiliation:
INRIA Saclay, ENS Cachan, LSV
SANTIAGO FIGUEIRA*
Affiliation:
Departamento de Computación, FCEyN, UBA and CONICET
SERGIO MERA*
Affiliation:
Departamento de Computación, FCEyN, UBA
*
*CARLOS ARECES, INRIA NANCY GRAND EST NANCY, FRANCE. E-mail:carlos.areces@gmail.com
DIEGO FIGUEIRA, INRIA SACLAY, ENS CACHAN, LSV CACHAN, FRANCE. E-mail:Figueira@lsv.ens-cachan.fr
SANTIAGO FIGUEIRA, DEPARTAMENTO DE COMPUTACIÓN, FCEyN, UNIVERSIDAD DE BUENOS AIRES BUENOS AIRES, ARGENTINA CONSEJO NACIONAL DE INVESTIGACIONES CIENTÍFICAS Y TÉCNICAS (CONICET), ARGENTINA. E-mail:sfigueir@dc.uba.ar
§SERGIO MERA, DEPARTAMENTO DE COMPUTACIÓN, FCEyN, UNIVERSIDAD DE BUENOS AIRES BUENOS AIRES, ARGENTINA. E-mail:smera@dc.uba.ar

Abstract

We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic ℋℒ (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.

This work focuses in the case where the memory is a set, and we can test whether the current node belongs to the set or not. We prove that, in terms of expressive power, the memory logics we discuss here lie between the basic modal logic and ℋℒ (↓). We show that the satisfiability problem of most of the logics we cover is undecidable. The only logic with a decidable satisfiability problem is obtained by imposing strong constraints on which elements can be memorized.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2011

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