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PRESERVATION OF ADMISSIBLE RULES WHEN COMBINING LOGICS

  • JOÃO RASGA (a1), CRISTINA SERNADAS (a1) and AMÍLCAR SERNADAS (a1)
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.

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Corresponding author
*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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