Combining Logics

New SEP entry on Combining Logics by Walter Carnielli and Marcelo Esteban Coniglio:

The subject of combinations of logics is still a young topic of contemporary logic. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there exist also many pragmatical and methodological reasons for considering combined logics. In fact, the use of formal logic as a tool for knowledge representation in Computer Science frequently requires the integration of several logic systems into a homogeneous environment. Important questions in the philosophy of logic such as: “why there are so many logics instead of just one?”(or even, instead of none), as e.g., raised in Epstein 1995, can be naturally counterposed by several other questions: if there are indeed many logics, are they excluding alternatives, or are they compatible? Is it possible to combine different logics into coherent systems with the purpose of using them in applications and to shed some light on the properties of complex logics? Moreover, if we can compose logics, why not decompose them? And, if a logic is decomposed into elementary sublogics, is it possible to recover it by combining such fragments? What kind of properties of logics can be transferred to their combinations? Questions of this kind have been only partially tackled in the literature, and reflect challenges to be confronted in the evolution of this topic.

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