# Boolean algebras of conditionals, probability and logic

```@article{Flaminio2020BooleanAO,
title={Boolean algebras of conditionals, probability and logic},
author={Tommaso Flaminio and Llu{\'i}s Godo and Hykel Hosni},
journal={ArXiv},
year={2020},
volume={abs/2006.04673}
}```
• Published 8 June 2020
• Computer Science, Mathematics, Philosophy
• ArXiv

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## References

SHOWING 1-10 OF 103 REFERENCES

### On Boolean Algebras of Conditionals and Their Logical Counterpart

• Mathematics
ECSQARU
• 2017
The logic of Boolean conditionals (LBC) is introduced and its completeness is proved with respect to the natural semantics induced by the structural properties of the atoms in a conditional algebra.

### Probability and Conditionals

The probability calculus is interpreted as a semantics for truth functional logic and conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent.

### Conditional inference and logic for intelligent systems - a theory of measure-free conditioning

• Computer Science
• 1991
This book discusses thegebraic structure of Conditional Events, an abstraction of the space of conditional events, and the role of Boolean algebras and Lewis' triviality result in its development.

### Stone Algebras, Conditional Events, and Three Valued Logic

• E. Walker
• Philosophy
IEEE Trans. Syst. Man Cybern. Syst.
• 1994
There are many ways to extend the operations on events to operations on conditional events, but it is shown that there is only one way to make such extensions so that the resulting structure is a bounded lattice extension of the space of events.

### Conditional Objects as Nonmonotonic Consequence Relationships

• Philosophy
IEEE Trans. Syst. Man Cybern. Syst.
• 1994
This paper investigates the relationship between conditional objects obtained as a qualitative counterpart to conditional probabilities, and nonmonotonic reasoning, and proposes a logic of conditional objects that is more elementary and intuitive than the preferential semantics of Lehmann and colleagues and does not require probabilistic semantics.

### Measure-Free Conditioning, Probability and Non-Monotonic Reasoning

• Philosophy
IJCAI
• 1989
It is shown that measure-free conditionals have the properties of well-behaved non-monotonic inference rules and can be useful to justify Cox's axiomatic framework for probability.

### On the Algebraic Structure of Conditional Events

• Mathematics
ECSQARU
• 2015
This paper investigates the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which the authors can be attached to them.

### Probabilistic Logic in a Coherent Setting

• Computer Science
• 2002
This paper presents a meta-analyses of Decomposable Measures of Uncertainty and their applications to Coherent Conditional Probability and Default Reasoning, and some of the implications of these studies are described.