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PRESERVATION OF ADMISSIBLE RULES WHEN COMBINING LOGICS

Published online by Cambridge University Press:  17 August 2016

JOÃO RASGA ,
CRISTINA SERNADAS  and
AMÍLCAR SERNADAS
JOÃO RASGA*
Affiliation:
Departamento de Matemática, Universidade de Lisboa
CRISTINA SERNADAS*
Affiliation:
Departamento de Matemática, Universidade de Lisboa
AMÍLCAR SERNADAS*
Affiliation:
Departamento de Matemática, Universidade de Lisboa
*
*DEPARTAMENTO DE MATEMÁTICA INSTITUTO SUPERIOR TÉCNICO AV. ROVISCO PAIS 1, 1049-001 LISBOA, PORTUGAL E-mail: jfr@math.tecnico.ulisboa.pt
†DEPARTAMENTO DE MATEMÁTICA INSTITUTO SUPERIOR TÉCNICO AV. ROVISCO PAIS 1, 1049-001 LISBOA, PORTUGAL E-mail: css@math.tecnico.ulisboa.pt
‡DEPARTAMENTO DE MATEMÁTICA INSTITUTO SUPERIOR TÉCNICO AV. ROVISCO PAIS 1, 1049-001 LISBOA, PORTUGAL E-mail: acs@math.tecnico.ulisboa.pt
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Abstract

Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics, under mild conditions. A weak form of structural completeness is proved to be preserved by the combination. Decidability of the set of admissible rules is also shown to be preserved, with no penalty on the time complexity. Examples are provided for the meet-combination of intermediate and modal logics.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 4 , December 2016 , pp. 641 - 663
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

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