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

A Measure-Free Approach to Conditioning