Preferential Structures for Comparative Probabilistic Reasoning
- URL: http://arxiv.org/abs/2104.02287v1
- Date: Tue, 6 Apr 2021 05:00:20 GMT
- Title: Preferential Structures for Comparative Probabilistic Reasoning
- Authors: Matthew Harrison-Trainor, Wesley H. Holliday, and Thomas F. Icard III
- Abstract summary: We show that a natural modification of the preferential approach yields exactly the same logical system as a probabilistic approach.
The same preferential structures used in the study of non-monotonic logics and belief revision may be used in the study of comparative probabilistic reasoning.
- Score: 2.0646127669654826
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Qualitative and quantitative approaches to reasoning about uncertainty can
lead to different logical systems for formalizing such reasoning, even when the
language for expressing uncertainty is the same. In the case of reasoning about
relative likelihood, with statements of the form $\varphi\succsim\psi$
expressing that $\varphi$ is at least as likely as $\psi$, a standard
qualitative approach using preordered preferential structures yields a
dramatically different logical system than a quantitative approach using
probability measures. In fact, the standard preferential approach validates
principles of reasoning that are incorrect from a probabilistic point of view.
However, in this paper we show that a natural modification of the preferential
approach yields exactly the same logical system as a probabilistic
approach--not using single probability measures, but rather sets of probability
measures. Thus, the same preferential structures used in the study of
non-monotonic logics and belief revision may be used in the study of
comparative probabilistic reasoning based on imprecise probabilities.
Related papers
- Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences.
Our method is especially suitable for problems with well-specified likelihoods.
We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
arXiv Detail & Related papers (2023-11-08T00:10:21Z) - Model-Agnostic Covariate-Assisted Inference on Partially Identified
Causal Effects [2.1638817206926855]
Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes.
We propose a unified and model-agnostic inferential approach for a wide class of partially identified estimands.
arXiv Detail & Related papers (2023-10-12T08:17:30Z) - A Robustness Analysis of Blind Source Separation [91.3755431537592]
Blind source separation (BSS) aims to recover an unobserved signal from its mixture $X=f(S)$ under the condition that the transformation $f$ is invertible but unknown.
We present a general framework for analysing such violations and quantifying their impact on the blind recovery of $S$ from $X$.
We show that a generic BSS-solution in response to general deviations from its defining structural assumptions can be profitably analysed in the form of explicit continuity guarantees.
arXiv Detail & Related papers (2023-03-17T16:30:51Z) - $\omega$PAP Spaces: Reasoning Denotationally About Higher-Order,
Recursive Probabilistic and Differentiable Programs [64.25762042361839]
$omega$PAP spaces are spaces for reasoning denotationally about expressive differentiable and probabilistic programming languages.
Our semantics is general enough to assign meanings to most practical probabilistic and differentiable programs.
We establish the almost-everywhere differentiability of probabilistic programs' trace density functions.
arXiv Detail & Related papers (2023-02-21T12:50:05Z) - Probabilistic Deduction: an Approach to Probabilistic Structured
Argumentation [1.027974860479791]
Probabilistic Deduction (PD) is an approach to probabilistic structured argumentation.
PD provides a framework to unify probabilistic reasoning with argumentative reasoning.
This is the first work in probabilistic structured argumentation where the joint distribution is not assumed form external sources.
arXiv Detail & Related papers (2022-09-01T03:58:38Z) - Logical Satisfiability of Counterfactuals for Faithful Explanations in
NLI [60.142926537264714]
We introduce the methodology of Faithfulness-through-Counterfactuals.
It generates a counterfactual hypothesis based on the logical predicates expressed in the explanation.
It then evaluates if the model's prediction on the counterfactual is consistent with that expressed logic.
arXiv Detail & Related papers (2022-05-25T03:40:59Z) - A Logic-based Tractable Approximation of Probability [0.0]
We identify the conditions under which propositional probability functions can be approximated by a hierarchy of depth-bounded Belief functions.
We show that our approximations of probability lead to uncertain reasoning which, under the usual assumptions in the field, qualifies as tractable.
arXiv Detail & Related papers (2022-05-06T13:25:12Z) - The intersection probability: betting with probability intervals [7.655239948659381]
We propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty.
We outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.
arXiv Detail & Related papers (2022-01-05T17:35:06Z) - Logical Credal Networks [87.25387518070411]
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability.
We investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud.
arXiv Detail & Related papers (2021-09-25T00:00:47Z) - Invariant Rationalization [84.1861516092232]
A typical rationalization criterion, i.e. maximum mutual information (MMI), finds the rationale that maximizes the prediction performance based only on the rationale.
We introduce a game-theoretic invariant rationalization criterion where the rationales are constrained to enable the same predictor to be optimal across different environments.
We show both theoretically and empirically that the proposed rationales can rule out spurious correlations, generalize better to different test scenarios, and align better with human judgments.
arXiv Detail & Related papers (2020-03-22T00:50:27Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.