Probabilistic reasoning in a classical logic

K. S. Ng; J. W. Lloyd

doi:10.1016/j.jal.2007.11.008

Probabilistic reasoning in a classical logic

K. S. Ng^*, J. W. Lloyd

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We offer a view on how probability is related to logic. Specifically, we argue against the widely held belief that standard classical logics have no direct way of modelling the certainty of assumptions in theories and no direct way of stating the certainty of theorems proved from these (uncertain) assumptions. The argument rests on the observation that probability densities, being functions, can be represented and reasoned with naturally and directly in (classical) higher-order logic.

Original language	English
Pages (from-to)	218-238
Number of pages	21
Journal	Journal of Applied Logic
Volume	7
Issue number	2
DOIs	https://doi.org/10.1016/j.jal.2007.11.008
Publication status	Published - Jun 2009

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AB - We offer a view on how probability is related to logic. Specifically, we argue against the widely held belief that standard classical logics have no direct way of modelling the certainty of assumptions in theories and no direct way of stating the certainty of theorems proved from these (uncertain) assumptions. The argument rests on the observation that probability densities, being functions, can be represented and reasoned with naturally and directly in (classical) higher-order logic.

KW - Classical logic

KW - Higher-order logic

KW - Integrating logic and probability

KW - Probabilistic reasoning

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Probabilistic reasoning in a classical logic

Abstract

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