@MISC{Hillman98aformal, author = {Chris Hillman}, title = {A Formal Theory Of Information: I. Statics}, year = {1998} }

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Abstract

this paper, I study "entropy" as a quantity defined axiomatically by certain formal properties, independently of any particular mathematical context. In particular, unlike all previous attempts to axiomatize information theory which are known to me, the concept of probability will play no role in the formal theory. I will define the notion of a joinset (essentially a lattice without the meet operation) and the notion of an entropy valuation on a joinset, which is a function assigning a non-negative real number to every element of the joinset, subject to three simple axioms to be given below. I will explain how, given an entropy valuation, we immediately obtain conditional and interaction entropies defined on pairs of elements, and I will show that this suite of entropies has all the formal properties of Shannon's probabilistic entropy (see [3][16]). In particular, we have notions of