Abstract
We examine some old and new paradoxes of probability, give a rough account of probabilistic conditionals, and prove a new result about non-monotonicity in probabilistic conditionals. It is well known that such conditionals are not monotonic – a conditional which is true can become false when additional hypotheses are added. We show that nonetheless, the conditionals are usually monotonic, or roughly speaking that we do not actually have to worry about non-monotonicity in practice.
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Dedicated to Anil Nerode on his 75th birthday. Research supported in part by a grant from PSC-CUNY grants program. Versions of this paper were given in colloquia at Boston University, CUNY Graduate Center, and at IHPST in Paris.
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Parikh, R. (2007). Some Puzzles About Probability and Probabilistic Conditionals . In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_31
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DOI: https://doi.org/10.1007/978-3-540-72734-7_31
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