
On Nonmonotonic Conditional Reasoning
This note is concerned with a formal analysis of the problem of nonmono...
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Extending and Automating Basic Probability Theory with Propositional Computability Logic
Classical probability theory is formulated using sets. In this paper, we...
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DempsterShafer vs. Probabilistic Logic
The combination of evidence in DempsterShafer theory is compared with t...
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Basic Formal Properties of A Relational Model of The Mathematical Theory of Evidence
The paper presents a novel view of the DempsterShafer belief function a...
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Extension of Boolean algebra by a Bayesian operator; application to the definition of a Deterministic Bayesian Logic
This work contributes to the domains of Boolean algebra and of Bayesian ...
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A Class of DSm Conditional Rules
In this paper we introduce two new DSm fusion conditioning rules with ex...
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Probability Logic
This chapter presents probability logic as a rationality framework for h...
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A MeasureFree Approach to Conditioning
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 knowledgebased 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 nonunique 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 oftenused 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.
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