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PROBABILITY FORMALIZATION IN TYPE THEORY: BRIDGING THEORY AND APPLICATION

Sophia Smith , Department of Mathematical Sciences, Auckland University of Technology, New Zealand

Abstract

Probability theory plays a fundamental role in modeling uncertainty and reasoning under uncertainty in various domains. Integrating probability concepts within type theory offers a formal framework to reason about probabilistic phenomena rigorously. This paper explores the formalization of probability concepts within type theory, aiming to bridge theoretical foundations with practical applications. We review foundational aspects of probability theory, discuss their formal representation in type theory, and highlight applications across computer science, artificial intelligence, and mathematical logic. Through illustrative examples and theoretical insights, we demonstrate how this integration enhances precision in probabilistic reasoning and supports the development of verifiable and reliable systems. This research contributes to advancing the theoretical underpinnings of probabilistic type theory and its practical implications for complex reasoning tasks in computational sciences.

Keywords

Probability theory, Type theory, Formalization

References

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Moreira, D.A.C.V., 2012. Finite probability distributions in Coq. mei.di.uminho.pt/sites/default/files/dissertacoes//eeu m_di_dissertacao_pg16019.pdf

Nederpelt, R. and H. Geuvers, 2014. Type Theory and Formal Proof. 1st Edn., Cambridge University Press, ISBN-10: 110703650X, pp: 436.

Rosenthal, J.S., 2006. A First Look at Rigorous Probability Theory. 2nd Edn., World Scientific, Singapore, ISBN-10: 9812703713, pp: 219.

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PROBABILITY FORMALIZATION IN TYPE THEORY: BRIDGING THEORY AND APPLICATION . (2024). International Journal of Mathematics and Statistics, 4(01), 10-14. https://www.academicpublishers.org/journals/index.php/ijmse/article/view/968