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Synthesis of Second-Order Equational Logic

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If you have a question about this talk, please contact Richard Garner.

I will present a mathematical methodology for the synthesis of equational deduction systems that are sound and internally complete for a canonical algebraic model theory; see [1].

As a running example, I will indicate how the methodology applies to rationally reconstruct the traditional equational logic of universal algebra from categorical principles; see [3 (Part I)].

As for a modern application, I will use the methodology to synthesise a second-order equational logic for specifying simple type theories; see [2 (Part I)] and [3 (Part II)].

This is joint work with Chung-Kil Hur.

References

[1] Marcelo Fiore and Chung-Kil Hur. Term equational systems and logics. In 24th Mathematical Foundations of Programming Semantics Conf. (MFPS XXIV ), 2008.

Paper

[2] Marcelo Fiore. Second-order and dependently-sorted abstract syntax. In Logic in Computer Science Conf. (LICS’08), pages 57-68. IEEE , Computer Society Press, 2008.

Paper

Slides

[3] Marcelo Fiore. Algebraic theories and equational logics. Invited tutorial at the 24th Mathematical Foundations of Programming Semantics Conf. (MFPS XXIV ), 2008.

Notes

This talk is part of the Category Theory Seminar series.

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