Inference in conditional probability logic

Niki Pfeifer; Gernot D. Kleiter

Kybernetika (2006)

  • Volume: 42, Issue: 4, page 391-404
  • ISSN: 0023-5954

Abstract

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An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if ..., then ...” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval [ 0 , 1 ] . Not all logically valid inference rules are probabilistically informative and vice versa. The relationship between logically valid and probabilistically informative inference rules is discussed and illustrated by examples such as the modus ponens or the affirming the consequent. We propose a method to evaluate the strength of CPL inference rules. Finally, an example of a proof is given that is purely based on CPL inference rules.

How to cite

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Pfeifer, Niki, and Kleiter, Gernot D.. "Inference in conditional probability logic." Kybernetika 42.4 (2006): 391-404. <http://eudml.org/doc/33813>.

@article{Pfeifer2006,
abstract = {An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if ..., then ...” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval $[0,1]$. Not all logically valid inference rules are probabilistically informative and vice versa. The relationship between logically valid and probabilistically informative inference rules is discussed and illustrated by examples such as the modus ponens or the affirming the consequent. We propose a method to evaluate the strength of CPL inference rules. Finally, an example of a proof is given that is purely based on CPL inference rules.},
author = {Pfeifer, Niki, Kleiter, Gernot D.},
journal = {Kybernetika},
keywords = {probability logic; conditional; modus ponens; system p; probability logic; conditional; modus ponens},
language = {eng},
number = {4},
pages = {391-404},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Inference in conditional probability logic},
url = {http://eudml.org/doc/33813},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Pfeifer, Niki
AU - Kleiter, Gernot D.
TI - Inference in conditional probability logic
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 4
SP - 391
EP - 404
AB - An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if ..., then ...” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval $[0,1]$. Not all logically valid inference rules are probabilistically informative and vice versa. The relationship between logically valid and probabilistically informative inference rules is discussed and illustrated by examples such as the modus ponens or the affirming the consequent. We propose a method to evaluate the strength of CPL inference rules. Finally, an example of a proof is given that is purely based on CPL inference rules.
LA - eng
KW - probability logic; conditional; modus ponens; system p; probability logic; conditional; modus ponens
UR - http://eudml.org/doc/33813
ER -

References

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