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Maximum Entropy As A Feasible Way To Describe Joint Distributions In Expert Systems, Thongchai Dumrongpokaphan, Vladik Kreinovich, Hung T. Nguyen
Maximum Entropy As A Feasible Way To Describe Joint Distributions In Expert Systems, Thongchai Dumrongpokaphan, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
In expert systems, we elicit the probabilities of different statements from the experts. However, to adequately use the expert system, we also need to know the probabilities of different propositional combinations of the experts' statements -- i.e., we need to know the corresponding joint distribution. The problem is that there are exponentially many such combinations, and it is not practically possible to elicit all their probabilities from the experts. So, we need to estimate this joint distribution based on the available information. For this purpose, many practitioners use heuristic approaches -- e.g., the t-norm approach of fuzzy logic. However, this …
A Natural Feasible Algorithm That Checks Satisfiability Of 2-Cnf Formulas And, If The Formulas Is Satisfiable, Finds A Satisfying Vector, Olga Kosheleva, Vladik Kreinovich
A Natural Feasible Algorithm That Checks Satisfiability Of 2-Cnf Formulas And, If The Formulas Is Satisfiable, Finds A Satisfying Vector, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main results in Theory of Computation courses is the proof that propositional satisfiability is NP-complete. This means that, unless P = NP (which most computer scientists believe to be impossible), no feasible algorithm is possible for solving propositional satisfiability problems. This result is usually proved on the example of 3-CNF formulas, i.e., formulas of the type C1 & ... & Cm, where each clause Ci has the form a \/ b or a \/ b \/ c, with no more than three literals -- i.e., propositional variables vi or their negations ~v …