HVW and Symbolic Projection Theory

In the 2D space, (S_xR, S_yR) is exactly the same as the pair of symbolic projections (u,v).

For time slice C_t₁ its x-projection is: S_xC_t₁ = S_x(x₁,x₂)C_t₁ = (u: a < b)
and its y-projection is: S_yC_t₁ = S_y(y₁,y₂)C_t₁ = (v: b < a)
The query S_t (t₁, t₂, t₃) R = (t: C_t₁ < C_t₂ < C_t₃)
The query S_x (x₁^o, x₂^o) (S_t (t₁, t₂, t₃) R) = (t: (u:a<b) < (u:a<b) < (u:a<b))

CHALLENGE: Hypermapped Virtual World Query can be translated into generalized symbolic projections for visual reasoning with respect to the HVW-enhanced Infosleuth's ontology model.

Note: The italized operator S indicates that the encoding is done according to the information-loseless default clustering mechanism. We can write S_x = S_x (x₁, ..., x_n). We will also use the notation * to indicate default clustering: S_x = S_x(*).

HVW and Symbolic Projection Theory

In the 2D space, (SxR, SyR) is exactly the same as the pair of symbolic projections (u,v).

For time slice Ct1 its x-projection is: SxCt1 = Sx(x1,x2)Ct1 = (u: a < b) and its y-projection is: SyCt1 = Sy(y1,y2)Ct1 = (v: b < a) The query St (t1, t2, t3) R = (t: Ct1 < Ct2 < Ct3) The query Sx (x1o, x2o) (St (t1, t2, t3) R) = (t: (u:a<b) < (u:a<b) < (u:a<b))

CHALLENGE: Hypermapped Virtual World Query can be translated into generalized symbolic projections for visual reasoning with respect to the HVW-enhanced Infosleuth's ontology model.

In the 2D space, (S_xR, S_yR) is exactly the same as the pair of symbolic projections (u,v).