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The Future of Logic: Foundation-Independence

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Abstract

Throughout the twentieth century, the automation of formal logics in computers has created unprecedented potential for practical applications of logic—most prominently the mechanical verification of mathematics and software. But the high cost of these applications makes them infeasible but for a few flagship projects, and even those are negligible compared to the ever-rising needs for verification. One of the biggest challenges in the future of logic will be to enable applications at much larger scales and simultaneously at much lower costs. This will require a far more efficient allocation of resources. Wherever possible, theoretical and practical results must be formulated generically so that they can be instantiated to arbitrary logics; this will allow reusing results in the face of today’s multitude of application-oriented and therefore diverging logical systems. Moreover, the software engineering problems concerning automation support must be decoupled from the theoretical problems of designing logics and calculi; this will allow researchers outside or at the fringe of logic to contribute scalable logic-independent tools. Anticipating these needs, the author has developed the Mmt framework. It offers a modern approach towards defining, analyzing, implementing, and applying logics that focuses on modular design and logic-independent results. This paper summarizes the ideas behind and the results about Mmt. It focuses on showing how Mmt. provides a theoretical and practical framework for the future of logic.

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  1. Jacobs University, Campus Ring 1, 28759, Bremen, Germany

    Florian Rabe

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  1. Florian Rabe
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Correspondence to Florian Rabe.

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The author was supported by DFG Grant RA-18723-1 OAF.

This paper won the prize of the UNILOG’2015 contest, The Future of Logic: http://www.uni-log.org/future-of-logic.

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Rabe, F. The Future of Logic: Foundation-Independence. Log. Univers. 10, 1–20 (2016). https://doi.org/10.1007/s11787-015-0132-x

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