Logical Foundations of Probability
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Logical Foundations of Probability By Rudolf Carnap Pp xvii + 607 (London: Routledge and Kegan Paul, Ltd, 1951) 42s net as mentioned in this paperAbstract:
Logical Foundations of Probability By Rudolf Carnap Pp xvii + 607 (London: Routledge and Kegan Paul, Ltd, 1951) 42s netread more
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An Introduction to Kolmogorov Complexity and Its Applications
Ming Li,Paul M. B. Vitányi +1 more
TL;DR: The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics.
Journal ArticleDOI
A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory
A. De Luca,Settimo Termini +1 more
TL;DR: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.
Journal ArticleDOI
A Formal Theory of Inductive Inference. Part II
TL;DR: Four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction.
Book
Possibilistic logic
D. Dubois,Jérôme Lang,H. Prade +2 more
TL;DR: Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete evidence and partially inconsistent knowledge that handles formulas of propositional or first-order logic to which are attached numbers between 0 and 1.
Journal ArticleDOI
Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning
Mike Oaksford,Nick Chater +1 more
TL;DR: The case is made that cognition in general, and human everyday reasoning in particular, is best viewed as solving probabilistic, rather than logical, inference problems, and the wider “probabilistic turn” in cognitive science and artificial intelligence is considered.
References
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Journal ArticleDOI
A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory
A. De Luca,Settimo Termini +1 more
TL;DR: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.
Journal ArticleDOI
A Formal Theory of Inductive Inference. Part II
TL;DR: Four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction.
Book
Possibilistic logic
D. Dubois,Jérôme Lang,H. Prade +2 more
TL;DR: Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete evidence and partially inconsistent knowledge that handles formulas of propositional or first-order logic to which are attached numbers between 0 and 1.
Journal ArticleDOI
A logic for reasoning about probabilities
TL;DR: In both cases, an elegant complete axiomization is provided, and it is shown that the problem of deciding satisfiability is NP-complete.
Book
Bayesian Rationality: The Probabilistic Approach to Human Reasoning
Mike Oaksford,Nick Chater +1 more
TL;DR: The authors argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in logic, and proposes that the Western conception of the mind as a logical system is flawed at the very outset.