Journal ArticleDOI
Probability and Conditionals
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The probability calculus is interpreted as a semantics for truth functional logic and conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent.Abstract:
The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second the probability calculus is extended in order to provide an interpretation for counterfactual probabilities — conditional probabilities where the condition has zero probability. Third, conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent. An axiom system for this conditional connective is recovered from the probabilistic definition. Finally, the primary semantics for this axiom system, presented elsewhere, is related to the probabilistic interpretation.read more
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Book ChapterDOI
Probabilities of Conditionals and Conditional Probabilities
TL;DR: The truthful speaker wants not to assert falsehoods, wherefore he is willing to assert only what he takes to be very probably true as discussed by the authors, where assertability goes by subjective probability.
Journal ArticleDOI
Conditionals: A Theory of Meaning, Pragmatics, and Inference
TL;DR: In a celebrated trial, Harr as discussed by the authors elicited the following information from an expert witness about the source of a chemical pollutant trichloroethylene (TCE): If the TCE in the wells had been drawn from out of the river, then there would be TCE on the riverbed. But there was no TCE at all.
Journal ArticleDOI
PRUF—a meaning representation language for natural languages
TL;DR: In addition to serving as a foundation for approximate reasoning, PRUF may be employed as a language for the representation of imprecise knowledge and as a means of precisiation of fuzzy propositions expressed in a natural language.
Book
The Geometry of Information Retrieval
TL;DR: The geometry of IR is studied through the lens of linear algebra, quantum mechanics, and vector and Hilbert spaces, with a focus on linear transformations, operators and matrices.
Proceedings ArticleDOI
Word sense disambiguation and information retrieval
TL;DR: From these results it has become clear that more basic research is needed to investigate the relationship between sense ambiguity, disambiguation, and IR.
References
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Book
The Logic of Scientific Discovery
TL;DR: The Open Society and Its Enemies as discussed by the authors is regarded as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day, as well as many of the ideas in the book.
Book ChapterDOI
A Theory of Conditionals
TL;DR: A conditional sentence expresses a proposition which is a function of two other propositions, yet not one which is truth function of those propositions as mentioned in this paper, which has given rise to a number of philosophical problems.
Book
The logic of conditionals
TL;DR: In this paper, it is argued that P.C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn.