Recent Trends in Algebraic Development Techniques

Volume 2755 of the series Lecture Notes in Computer Science pp 185-200

Completeness Results for Fibred Parchments

  • C. CaleiroAffiliated withCLC – Departamento de Matemática, IST – UTL
  • , P. GouveiaAffiliated withCLC – Departamento de Matemática, IST – UTL
  • , J. RamosAffiliated withCLC – Departamento de Matemática, IST – UTL

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In [6] it was shown that fibring could be used to combine institutions presented as c-parchments, and several completeness preservation results were established. However, their scope of applicability was limited to propositional-based logics. Herein, we extend these results to a broader class of logics, possibly including variables, terms and quantifiers. On the way, we need to consider an enriched notion of proof-calculus that deals explicitly with the substitution provisos that often appear in schematic inference rules. For illustration of the concepts, constructions and results, we shall adopt modal first-order logic as a working example.