Hello! I'm Brian.
Recently I returned to the USA after finishing a dual masters degree in Pure Mathematics as part of the European Erasmus Mundus ALGANT (ALgebra Geometry And Number Theory) program and have studied around the world (Italy, India, Netherlands).
Currently I am working on several papers. Nearing completion is a paper titled: "Propositional Logic and Correspondence Matrices" (CM's) In which I developed `Correspondence Matrices' which correspond to logical operators in propositional logic. I extend the notion of CM's to general logical matrices in higher dimensions, show that they are linear and extend the notion of measurement (such as is used in quantum theory) to both compute and find relationships between logical expressions. Furthermore I developed a novel algorithm which allows the composition of general logical expressions.
In other papers I am currently investigating Topological spaces built propositional logic as well as a logical homology and construction of simplicial complexes built on logical expressions. I have also developed a way to use the logistic function (machine learning) to evolve logical expressions.
In my work in propositional logic I am pursuing two areas; the first consists of tools (Topologies and Homologies etc.) which I am using to model the notion of a `mental space' as I aim in helping to map `thought processes' with the underlying neurobiological processes. The second area is to build a quantum logical framework which I can interface with other tools which I have built to model the ideas of psychoanalyst Ignacio Matte-Blanco to model his notion of consciousness.