A simplified duality for implicative lattices and l-groups

Studia Logica ◽  
1996 ◽  
Vol 56 (1-2) ◽  
pp. 185-204 ◽  
Author(s):  
Nestor G. Martinez
Keyword(s):  
Implicative Lattices

Embeddings of implicative lattices and superintuitionistic logics

1987 ◽  
Vol 26 (3) ◽  
pp. 178-205 ◽  
Author(s):  
S. I. Mardaev
Keyword(s):  
Superintuitionistic Logics ◽  
Implicative Lattices

Quasi-Implicative Lattices and the Logic of Quantum Mechanics

1975 ◽  
Vol 30 (11) ◽  
pp. 1347-1360
Author(s):  
Gary M. Hardegree
Keyword(s):  
Quantum Mechanics ◽  
Orthocomplemented Lattice ◽  
Implicative Lattices ◽  
Necessary And Sufficient

Mittelstaedt has defined the class of quasi-implicative lattices and shown that an ortholattice (orthocomplemented lattice) is quasi-implicative exactly if it is orthomodular (quasi-modular). He has also shown that the quasi-implication operation is uniquely determined by the quasi-implicative conditions. One of Mittelstaedt's conditions, however, seems to lack immediate intuitive motivation. Consequently, this paper seeks to provide a number of reformulations of the quasi-implicative conditions which are more intuitively plausible. Three sets of conditions are examined, and it is shown that each set of conditions is both necessary and sufficient to ensure that an ortholattice is orthomodular, and each set of conditions uniquely specifies the implication operation to be Mittelstaedt's quasi-implication. Various properties of the quasi-implication are then investigated. In particular, it is shown that the quasi-implication fails to satisfy a number of laws associated with the classical material conditional. Various weakenings of these laws, satisfied by the quasi-implication, are also discussed

scholarly journals Meet-irreducible elements in implicative lattices

1972 ◽  
Vol 34 (1) ◽  
pp. 57-57 ◽  
Author(s):  
Dorothy P. Smith
Keyword(s):  
Irreducible Elements ◽  
Implicative Lattices

Atoms, Primes and Implicative Lattices

1984 ◽  
Vol 27 (3) ◽  
pp. 279-285
Author(s):  
C. S. Hoo
Keyword(s):  
Atomistic Lattice ◽  
Implicative Lattices

AbstractLet L be an a-implicative semilattice. We obtain a characterization of those elements which cover a. This gives a characterization of atoms in pseudocomplemented semilattices, and leads to various results on primes and irreducibles in semilattices. As an application, we prove that in a complete, atomistic lattice L, the following are equivalent (i) L is implicative (ii) L is (2, ∞) meet distributive (iii) each element of L is a meet of primes.

scholarly journals On Kalman’s functor for bounded hemi-implicative semilattices and hemi-implicative lattices

2017 ◽  
Vol 26 (1) ◽  
pp. 47-82
Author(s):  
Ramon Jansana ◽  
Hernán Javier San Martín
Keyword(s):  
Implicative Lattices ◽  
Implicative Semilattices
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