Definitions page 
* g: The entire graph of CGKB
* g_i, h: placeholder for any subgraph of g
* Contextualize: the Contextualize algorithm
* c_0: the initial context, determined from fn, i_p
* <fn, i_p>: the canonicalized input from the interface of HTMI page after parsing a human input, where fn is a TM function, and i_p the partial information needed for fn’s execution.
* filter: fields used to filter context, i.e. constrain the expansion of initial context in the Contexualize algorithm; thus far they are {privacy, entity, ranking, time, constraints, graph properties}
* scope: the lists of fulfilled and unfulfilled information, scope_f, i_u respectively for the extraction of i for fn(i).
* c: contextual (knowledge) graph, or the contextualized subgraph, i.e. the output Contextualize(g, c_0, i_p); c ⊂ g
* i ∈ I: the complete information needed to compute fn(i). It is encoded within g; obviously there exists a smallest subgraph h ⊂ g that sufficiently encodes i. Equivalently i is the union of partial information i_1, i_2, ...
* k: knowledge, i.e. the complete information extractable from g. Note i ⊂ k, but fn(i) = fn(k) since the TM function fn only computes using the needed information.
* k_h: the information extractable from subgraph h ⊂ g. Note k = k_g.
* Ex: the extraction operator to extract knowledge from a graph, e.g. k = Ex(g), k_h = Ex(h)
* -*->: graph path, or ‘derives’. We say g_1 -*-> g_2 if g_1 is connected to g_2, and k_1 -*-> k_2 if k_1 derives k_2.
Axioms
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1. Knowledge is encoded in a graph g, and decoded using the Ex operator. 2. Knowledge is deriverable, and this is reflected in its graph encoding by connectedness. Let k_1 = Ex(g_1), k_2 = Ex(g_2), if k_1 derives k_2, i.e. k_1 -*-> k_2, then there must exists a corresponding path g_1 -*-> g_2, s.t. (k_1 ∪ k_2) is extractable from the connected component CC of g_1, i.e. (k_1 ∪ k_2) ⊂ Ex(CC(g_1)). 3. Base knowledge (graph sink) is the most basic knowledge, and is the source of the derivation path. If the path is cyclic, arbitrarily choose the last-encountered node as the basic knowledge. Base knowledge resolves all knowledge along the derivation path by gradual substitutions.