  Carcinogenesis is a complex process that involves dynamically inter-connected
modular sub-networks that evolve under the influence of micro-environmentally
induced perturbations, in non-random, pseudo-Markov chain processes. An
appropriate n-stage model of carcinogenesis involves therefore n-valued Logic
treatments of nonlinear dynamic transformations of complex functional genomes
and cell interactomes. Lukasiewicz Algebraic Logic models of genetic networks
and signaling pathways in cells are formulated in terms of nonlinear dynamic
systems with n-state components that allow for the generalization of previous,
Boolean or "fuzzy", logic models of genetic activities in vivo. Such models are
then applied to cell transformations during carcinogenesis based on very
extensive genomic transcription and translation data from the CGAP databases
supported by NCI. Such models are represented in a Lukasiewicz-Topos with an
n-valued Lukasiewicz Algebraic Logics subobject classifier description that
represents non-random and nonlinear network activities as well as their
transformations in carcinogeness. Specific models for different types of cancer
are then derived from representations of the dynamic state-space of LT
non-random, pseudo-Markov chain process, network models in terms of cDNA and
proteomic, high throughput analyses by ultra-sensitive techniques. This novel
theoretical analysis is based on extensive CGAP genomic data for human tumors,
as well as recently published studies of cyclin signaling. Several such
specific models suggest novel clinical trials and rational therapies of cancer
through re-establishment of cell cycling inhibition in stage III cancers.

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