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Studia Logica

, Volume 101, Issue 4, pp 783–825 | Cite as

A Coalgebraic Perspective on Logical Interpretations

  • M. A. MartinsEmail author
  • A. Madeira
  • L. S. Barbosa
Article

Abstract

In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptation, difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new research avenue in program refinement, (conceptual) tools are needed to reason about them. In this line, the paper’s main contribution is a study of the correspondence between logical interpretations and morphisms of a particular kind of coalgebras. This opens way to the use of coalgebraic constructions, such as simulation and bisimulation, in the study of interpretations between (abstract) logics.

Keywords

Abstract logic Interpretation Coalgebra Program refinement 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.CIDMA, Dep. MathematicsUniversidade de AveiroAveiroPortugal
  2. 2.Critical Software, MAP-i Doctoral ProgrammeAveiroPortugal
  3. 3.HASLab \ INESC TECUniversidade do MinhoBragaPortugal

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