Probing the quantitative–qualitative divide in probabilistic reasoning

Ibeling, Duligur; Icard, Thomas; Mierzewski, Krzysztof; Mossé, Milan

doi:10.1016/j.apal.2023.103339

Search citation statements

Order By: Relevance

Paper Sections

Select...

Polynomials In Probabilities1

Citation Types

Supporting

Mentioning

Contrasting

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(This is in fact expressible already in L cond prob .) This enforces that P(B) = 1/ √ 2, while Ibeling et al [27] show that every formula in L lin prob has models in which every probability is rational.…”

Section: Polynomials In Probabilitiesmentioning

confidence: 98%

Is Causal Reasoning Harder Than Probabilistic Reasoning?

Mossé¹,

Ibeling²,

Icard³

2022

The Review of Symbolic Logic

View full text Add to dashboard Cite

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability.

show abstract

Section: Polynomials In Probabilitiesmentioning

confidence: 98%