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Conditional logic and the Principle of Entropy. (English) Zbl 0939.68854
Summary: The conditional three-valued logic of Calabrese is applied to the language \(L^{*}\) of conditionals on propositional variables with finite domain. The conditionals in \(L^{*}\) serve as a means for the construction and manipulation of probability distributions respecting the principle of maximum entropy and of minimum relative entropy. This principle allows a sound inference even in the presence of uncertain evidence. The inference is directed, it respects a probabilistic version of Modus Ponens – not of Modus Tollens –, it permits transitive chaining and supports a cautious monotony. Conjunctive, conditional and material deduction are manageable in this probabilistic logic, too. The concept is not merely theoretical, but enables large-scale applications in the expert system-shell SPIRIT.

MSC:
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68T27 Logic in artificial intelligence
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