Abstract
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a given base logic. These examples are surveyed in the paper under a particular perspective—that this sort of combination of logics possesses a functorial nature. Such a view gives rise to several interesting questions. They range from the problem of combining translations (between logics), to that of ensuring property preservation along the process, and the way different asymmetric combinations can be related through appropriate natural transformations.
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Notes
- 1.
\((\_)^{op}\) applied to a functor \(F : \mathbf {C} \rightarrow \mathbf {D}\) induces a functor \(F^{op} : \mathbf {C}^{op} \rightarrow \mathbf {D}^{op}\) such that for any object or arrow a in \(\mathbf {C}\), \(F^{op}(a) = F(a)\).
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Acknowledgments
This work is financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. Further support was provided by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement through the ERFD in the context of project NORTE-01-0145-FEDER-000037. Renato Neves was also sponsored by FCT grant SFRH/BD/52234/2013, and Alexandre Madeira by FCT grant SFRH/BPD/103004/2014.
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Neves, R., Madeira, A., Barbosa, L.S., Martins, M.A. (2017). Asymmetric Combination of Logics is Functorial: A Survey. In: James, P., Roggenbach, M. (eds) Recent Trends in Algebraic Development Techniques. WADT 2016. Lecture Notes in Computer Science(), vol 10644. Springer, Cham. https://doi.org/10.1007/978-3-319-72044-9_4
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