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1. • CommentRowNumber1.
   • CommentAuthorporton
   • CommentTimeJan 10th 2016
   • (edited Jan 10th 2016)
   • PermaLink
   Author: porton
   Format: MarkdownItexA new thought which I had less than a minute ago: Boolean lattices follow classical propositional logic. Heyting algebras follow intuitionistic logic. What about the logic for a system of two lattices: a "base" lattice and its sublattice? I study in details some properties of a poset and its subset (I call such a pair of two posets as "filtrator") in [my research monograph](http://www.mathematics21.org/algebraic-general-topology.html). I suspect that such "double" logic may be of relevance for my research. But I don't know how to formulate this vague thought exactly. Any ideas?

   A new thought which I had less than a minute ago:

   Boolean lattices follow classical propositional logic. Heyting algebras follow intuitionistic logic.

   What about the logic for a system of two lattices: a “base” lattice and its sublattice?

   I study in details some properties of a poset and its subset (I call such a pair of two posets as “filtrator”) in my research monograph.

   I suspect that such “double” logic may be of relevance for my research. But I don’t know how to formulate this vague thought exactly. Any ideas?

2. • CommentRowNumber2.
   • CommentAuthorporton
   • CommentTimeJan 10th 2016
   • PermaLink
   Author: porton
   Format: MarkdownItexNote that in most basic applications of my theory the base lattice is co-brouwerian and the "core" (that is the sub-lattice) lattice is boolean.

   Note that in most basic applications of my theory the base lattice is co-brouwerian and the “core” (that is the sub-lattice) lattice is boolean.