The Future of Logic: Foundation-Independence

Logica Universalis 10 (1):1-20 (2016)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Proof theory of modal logic.Heinrich Wansing (ed.) - 1996 - Boston: Kluwer Academic Publishers.
Modal Hybrid Logic.Andrzej Indrzejczak - 2007 - Logic and Logical Philosophy 16 (2-3):147-257.
Popular lectures on mathematical logic.Hao Wang - 1981 - New York: Dover Publications.
Goal-directed proof theory.Dov M. Gabbay - 2000 - Boston: Kluwer Academic. Edited by Nicola Olivetti.
The Semantics and Proof Theory of Linear Logic.Arnon Avron - 1988 - Theoretical Computer Science 57 (2):161-184.
Logic and Probability.Kenny Easwaran - 2010 - Journal of the Indian Council of Philosophical Research 27 (2):229-253.
The method of hypersequents in the proof theory of propositional non-classical logics.Arnon Avron - 1996 - In Wilfrid Hodges (ed.), Logic: Foundations to Applications. Oxford: pp. 1-32.
On empirical status of logical inferences.Marcin Mostowski - 1983 - Bulletin of the Section of Logic 12 (4):181-184.

Analytics

Added to PP
2015-12-12

Downloads
22 (#607,190)

6 months
2 (#670,035)

Historical graph of downloads
How can I increase my downloads?