Visualization in propositional logic

We are visually exploring a current problem in propositional logic related to information processing, specifically n-traces. Traces represent subsets of possible consequences which can be inferred classically from partitions of the set of inputs. We are interested in the relationship between a given set of Boolean inputs and its respective trace(s). Let Σ be a set of sentences or data. In particular, suppose that Σ represents information received by a central processor from N distinct channels. Each channel is self-consistent, but the distinct channels may supply conflicting data. Then Σ will contain no sentence of the form α∧~α, but it may contain both the sentences α and ~α. If the processor must draw inferences from Σ using methods of standard logic, then when separate channels supply conflicting information, the processor is justified in inferring every sentence of the language. To avoid this, we must give the processor some comparatively conservative inference strategy. One such strategy redeploys standard inferential methods in a way that introduces a relative measure of incoherence and provides a formulation for incoherence-tolerant inference. We define l(Σ), the incoherence level of Σ, as the cardinal of the least partition of Σ into consistent subsets. Then any sentence can be inferred from Σ if it is inferrable by standard methods from at least one element of every l(Σ)-partition of Σ. We define a set T^l that is an l(Σ)-trace over Σ for which the processor will infer β if β is a standard consequence of every element of T^l