ABSTRACT
A: X → Y , E: X → ¬Y , I: X ∧ Y , O: X ∧ ¬Y ,
Mechanical Logic in Three-Dimensional Space Gennaro Auletta Copyright c© 2014
September 13,
in explicit quantified form as in Table 1.4 but also that this is
unnecessary in such a context). Obviously, other choices are possible
but this changes nothing in the system (due to its symmetry). It is
also worth mentioning that these statements already occur in the
two-dimensional space (see Table 1.3). Then, I shall try to derive
these statements from more elementary ones. Moreover, I recall
that all statements have both a LGS and RGS and that the sum of
these two gives precisely to 8 generating elements for any statement
considered; for instance, {A} = {{A1, A2}, {A3, A4, A5, A6, A7, A8}}, where the first subset is the LGS whilst the second one is the RGS. Some of these elements will be introduced in this section,
some later. However, to avoid any confusion I present here three
summary tables that gives the connection between the number of
the statement and its associated symbol.
