Graduate studies at Western
Studia Logica 58 (3):403-450 (1997)
|Abstract||Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's  and Urquhart's ), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality.In part II, we consider lattice-ordered algebras (lattices with additional operators), extending the Jónsson and Tarski representation results  for Boolean algebras with Operators. Our work can be seen as developing, and indeed completing, Dunn's project of gaggle theory [13, 14]. We consider general lattices (rather than Boolean algebras), with a broad class of operators, which we dubb normal, and which includes the Jónsson-Tarski additive operators. Representation of l-algebras is extended to full duality.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Alasdair Urquhart (1979). Distributive Lattices with a Dual Homomorphic Operation. Studia Logica 38 (2):201 - 209.
David Hobby (1996). Semi-Demorgan Algebras. Studia Logica 56 (1-2):151 - 183.
Guram Bezhanishvili (1999). Varieties of Monadic Heyting Algebras Part II: Duality Theory. Studia Logica 62 (1):21-48.
Alejandro Petrovich (1996). Distributive Lattices with an Operator. Studia Logica 56 (1-2):205 - 224.
Yoshihiro Maruyama (2010). Fuzzy Topology and Łukasiewicz Logics From the Viewpoint of Duality Theory. Studia Logica 94 (2):245 - 269.
Viorica Sofronie-Stokkermans (2000). Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I. Studia Logica 64 (1):93-132.
Francesco Paoli, Matthew Spinks & Robert Veroff (2008). Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties. Logica Universalis 2 (2):209-233.
P. Garcia & F. Esteva (1995). On Ockham Algebras: Congruence Lattices and Subdirectly Irreducible Algebras. Studia Logica 55 (2):319 - 346.
Katalin Bimbó (2007). Functorial Duality for Ortholattices and de Morgan Lattices. Logica Universalis 1 (2):311-333.
Alasdair Urquhart (1996). Duality for Algebras of Relevant Logics. Studia Logica 56 (1-2):263 - 276.
Added to index2009-01-28
Total downloads9 ( #122,562 of 739,140 )
Recent downloads (6 months)2 ( #37,337 of 739,140 )
How can I increase my downloads?