Universal logic

Universal logic is the field of logic that is concerned with giving an account of what features are common to all logical structures. Universal logic aims to be to logic what universal algebra is to algebra; currently there is no universally accepted notion of logic (or logical system). Several frameworks have been proposed.

The term 'universal logic' was introduced in the 1990s by Swiss logician Jean-Yves Béziau, but the field has arguably existed for many decades.[1] Some of the works of Alfred Tarski in the early twentieth century, for example, can be regarded as fundamental contributions to universal logic.

Three model-theoretic directions for universal logic have been explored to some depth: abstract model theory axiomatized by Jon Barwise, a topological / categorical approach based on sketches (sometimes called categorical model theory), and yet another categorical approach based on Goguen and Burstall's notion of institution.[2]

The First World Congress and School on Universal Logic took place in Montreux, Switzerland in early 2005. Participants included Béziau, Dov Gabbay, Saul Kripke, and David Makinson.[3] A journal dedicated to the field, Logica Universalis, with Béziau as editor-in-chief started to be published by Birkhäuser Basel (an imprint of Springer) in 2007.[4] Springer also started to publish a book series on the topic, Studies in Universal Logic, with Béziau as series editor.[5]

The term 'universal logic' has also been used by some logicians (e.g. Richard Sylvan and Ross Brady) to refer to a new type of (weak) relevant logic.[6]

An anthology titled Universal Logic was published in 2012, giving a new light on the subject. [7]


See also

References

  1. ↑ Jean-Yves Béziau, ed. (2007). Logica universalis: towards a general theory of logic (2nd ed.). Springer. ISBN 978-3-7643-8353-4.
  2. ↑ Răzvan Diaconescu (2008). Institution-independent model theory. Birkhäuser. pp. 2–3. ISBN 978-3-7643-8707-5.
  3. ↑ UNILOG '05: First World Congress and School on Universal Logic
  4. ↑ http://www.springer.com/birkhauser/mathematics/journal/11787
  5. ↑ http://www.springer.com/series/7391
  6. ↑ Brady, R. 2006. Universal Logic. Stanford: CSLI Publications. ISBN 1-57586-255-7.
  7. ↑ Jean-Yves Béziau, ed. (2012). Universal Logic: an Anthology - Form Paul Hertz to Dov Gabbay. Springer. ISBN 978-3-0346-0144-3.

External links