Cancellative residuated lattices

By P. Bahls, J. Cole, Nikolaos Galatos, Peter Jipsen, C. Tsinakis. 2003

115 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/cb34b219ff35fb9734efabab31ab8bc8131b5606

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Peter Jipsen
2. Constantine Tsinakis
3. Franco Montagna
4. Nikolaos Galatos
5. George Metcalfe
6. Lavinia Corina Ciungu
7. Anatolij Dvurecenskij

In Management Science and Operations Research

1. Peter Jipsen
2. Constantine Tsinakis
3. Franco Montagna
4. Nikolaos Galatos
5. Anatolij Dvurecenskij
6. George Metcalfe
7. Lavinia Corina Ciungu

Citations in the corpus

• Minimal varieties of residuated lattices (2005, background): “It is easy to see that a residuated lattice is cancellative if and only if it satisfies the identities x\xy ≈ y ≈ yx/x, see [2], hence the class of all cancellative residuated lattices forms a variety.”
• Classes of residuated lattices (2006, background): “([1]) A residuated lattice is an algebra L = (L,∧,∨, ̄,→, Ã, 0, 1) of the type (2, 2, 2, 2, 2, 0, 0) satisfying the following conditions: (L1) (L,∧,∨, 0, 1) is a bounded lattice; (L2) (L, ̄, 1) is a non-commutative monoid; (L3) x ̄ y ≤ z iff x ≤ y → z iff y ≤ x à z for any x, y, z ∈ L.”
• Probabilistic Averaging in Bounded Rℓ-Monoids (2006, methodology): “A mapping s : M −→ [0, 1 ] is said to be a Bosbach state (or simply a state) if for all x, y ∈ M”
• Generalized MV-algebras (2005, methodology): “We tend to favor\ in calculations, but any statement about residuated structures has anopposite“mirror image” obtained by reading terms backwards (i.e., replacingx · y by y · x and interchangingx/y with y\x).”
• AMALGAMATION AND INTERPOLATION IN ORDERED ALGEBRAS (2014, background): “It is easily shown (see [5,8]) that the class of pointed residuated lattices forms a congruence distributive variety and that all the preceding conditions may be expressed equationally.”
• The Structure of Residuated Lattices (2003, background): “• Although in many well-known subvarieties of RL distributivity is a consequence of the cancellative law, this is not true in general (see [2]).”
• On the structure of generalized BL-algebras (2006, background): “1 0 denoting the least element of the algebra, together with the equations for residuated lattices, integral GBL-algebras, and prelinearity : 1 ≤ (x/y ∨ y/x) ∧ (x\y ∨ y\x).”
• A Survey of Residuated Lattices (2002, methodology): “For further discussion about this, we refer to [BCGJT].”