  One presents a simple Set Theory Model (STM) of the valid categorical
arguments (VCAs) - a proper superset of the valid (categorical) syllogisms
(VS). The main STM initiator was George Boole, who worked with a universe of
discourse, U, which contains the pairwise complementary sets, or categorical
terms, S, non-S, P, non-P, M, non-M, and is thus partitioned into eight
subsets: SPM, SP(non-M),...,(non-S)(non-P)(non-M), where the intersection was
denoted by adjacency. In STM all superfluous syllogistic figures are
disregarded, and both the positive terms, S, P, M, and the negative terms,
non-S, non-P, non-M, are allowed to appear in the pairs of categorical premises
(PCPs) and their entailed logical consequences (LCs). This increases the number
of distinct P (resp. S) premises from the six formulable via only positive
terms, to eight, and the number of distinct PCPs from the 36 appearing in the
Classical Categorical Syllogistic (CCS), to the 64 appearing in the STM. Out of
the latter 64 PCPs, only 32 PCPs entail LCs and thus generate VCAs. These VCAs,
(and the VS), split into four types. Each type contains eight VCAs. Any VCA can
be re-written as any other VCA of the same type, via a group G of eight
re-labelings. Thus the VCAs Barbara, Darapti, Darii, Disamis, can be chosen as
type representatives for both VCAs and VS, and via a term relabeling, any VCA
or VS can be re-written, without changing their PCP or LC contents, as either a
Barbara, Darapti, Darii, or Disamis. One discusses the VCAs and their LCs,
simple/biliteral VCA sorites, empty set constraints (ESC), VCA distribution
conservation, and other Rules of Valid Categorical Arguments (RofVCA) which are
VCA generalized versions of some of the Rules of Valid Syllogisms (RofVS). Note
that CCS restricts the VS to only LCs of the formats A(S,P), E(S,P), I(S,P),
O(S,P).
