  In an earlier paper, a new theory of measurefree "conditional" objects was
presented. In this paper, emphasis is placed upon the motivation of the theory.
The central part of this motivation is established through an example involving
a knowledge-based system. In order to evaluate combination of evidence for this
system, using observed data, auxiliary at tribute and diagnosis variables, and
inference rules connecting them, one must first choose an appropriate algebraic
logic description pair (ALDP): a formal language or syntax followed by a
compatible logic or semantic evaluation (or model). Three common choices- for
this highly non-unique choice - are briefly discussed, the logics being
Classical Logic, Fuzzy Logic, and Probability Logic. In all three,the key
operator representing implication for the inference rules is interpreted as the
often-used disjunction of a negation (b => a) = (b'v a), for any events a,b.
  However, another reasonable interpretation of the implication operator is
through the familiar form of probabilistic conditioning. But, it can be shown -
quite surprisingly - that the ALDP corresponding to Probability Logic cannot be
used as a rigorous basis for this interpretation! To fill this gap, a new ALDP
is constructed consisting of "conditional objects", extending ordinary
Probability Logic, and compatible with the desired conditional probability
interpretation of inference rules. It is shown also that this choice of ALDP
leads to feasible computations for the combination of evidence evaluation in
the example. In addition, a number of basic properties of conditional objects
and the resulting Conditional Probability Logic are given, including a
characterization property and a developed calculus of relations.
