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A new conceptual foundation for the notion of "information" is proposed,based on the concept of a "distinction graph": a graph in which two nodes areconnected iff they cannot be distinguished by a particular observer. The"graphtropy" of a distinction graph is defined as the average connectionprobability of two nodes; in the case where the distinction graph is a composedof disconnected components that are fully connected subgraphs, this isequivalent to Ellerman's logical entropy, which has straightforwardrelationships to Shannon entropy. Probabilistic distinction graphs andprobabilistic graphtropy are also considered, as well as connections betweengraphtropy and thermodynamic and quantum entropy. The semantics of the SecondLaw of Thermodynamics and the Maximum Entropy Production Principle are unfoldedin a novel way, via analysis of the cognitive processes underlying the makingof distinction graphs This evokes an interpretation in which complexintelligence is seen to correspond to states of consciousness with intermediategraphtropy, which are associated with memory imperfections that violate theassumptions leading to derivation of the Second Law. In the case where nodes ofa distinction graph are labeled by computable entities, graphtropy is shown tobe monotonically related to the average algorithmic information of the nodes(relative to to the algorithmic information of the observer). Aquantum-mechanical version of distinction graphs is considered, in whichdistinctions can exist in a superposed state; this yields to graphtropy as ameasure of the impurity of a mixed state, and to a concept of "quangraphtropy."Finally, a novel computational model called Dynamic Distinction Graphs (DDGs)is formulated, via enhancing distinction graphs with additional linksexpressing causal implications, enabling a distinction-based model of"observers."

Distinction Graphs and Graphtropy: A Formalized Phenomenological Layer  Underlying Classical and Quantum Entropy, Observational Semantics and  Cognitive Computation