Residuated Lattices for the Working Mathematician

Host Institution:

La Trobe University

Title of Seminar:

Residuated Lattices for the Working Mathematician

Speaker's Name:

Dr Tomasz Kowalski

Speaker's Institution:

La Trobe University

Time and Date:

Friday 27 April 2012, 2:00pm (AEST)

Seminar Abstract:

A residuated lattice is an algebra which combines a lattice and a monoid by means of residuation operations (left and right divisions). For example, the set of two-sided ideals in any ring forms a residuated lattice (this lattice was studied by Birkhoff in 1934, and I believe it was the very first residuated lattice to be discovered). In 1930s residuated lattices were investigated in a series of papers by Ward and Dilworth, but then not much happened until about 20 years ago, when residuated lattices were rediscovered by two very different groups of researchers:

  • algebraists (as a generalisation of lattice-ordered groups) and
  • logicians (as algebraic semantics for proof systems known as Gentzen calculi).

The theory of residuated lattices is to a large extent a result of interactions between these two groups. I will present some of that theory, trying to meet two largely incompatible conditions: (a) to be non-technical, (b) to focus on open problems.

Seminar Convenor:

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