Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Fuzzy sets, fuzzy logic, and fuzzy systems
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Foundations of statistical natural language processing
Foundations of statistical natural language processing
Speech Synthesis and Recognition
Speech Synthesis and Recognition
Reasoning about Uncertainty
Introducing Speech and Language Processing (Cambridge Introductions to Language and Linguistics)
Introducing Speech and Language Processing (Cambridge Introductions to Language and Linguistics)
Probabilistic Logic Networks: A Comprehensive Framework for Uncertain Inference
Probabilistic Logic Networks: A Comprehensive Framework for Uncertain Inference
Practical Markov logic containing first-order quantifiers with application to identity uncertainty
CHSLP '06 Proceedings of the Workshop on Computationally Hard Problems and Joint Inference in Speech and Language Processing
First-order conditional logic revisited
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
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Indefinite probabilities are a novel technique for quantifying uncertainty, which were created as part of the PLN (Probabilistic Logic Networks) logical inference engine, which is a key component of the Novamente Cognition Engine (NCE), an integrative AGI system. Previous papers have discussed the use of indefinite probabilities in the context of a variety of logical inference rules, but have omitted discussion of quantification. Here this gap is filled, and a mathematical procedure is provided allowing the propagation of indefinite probabilities through universal and existential quantifiers, and also through a variety of fuzzy quantifiers corresponding to natural language quantifiers (such as “few”, “many”, “a lot”, “hardly any”, etc.). Proper probabilistic handling of various quantifier transformation rules is also discussed. Together with the ideas in prior publications, and a forthcoming sequel paper on indefinite probabilities for intensional inference, these results allow probabilistic logic based on indefinite probabilities to be utilized for the full scope of inferences involved in intelligent reasoning. To illustrate the ideas and algorithms involved, we give two concrete examples: Halpern's “crooked lottery” predicate, and a commonsense syllogism that uses fuzzy quantifiers together with the standard PLN term logic deduction rule.