Probabilistic Deduction: an Approach to Probabilistic Structured Argumentation

• URL: http://arxiv.org/abs/2209.00210v1
• Date: Thu, 1 Sep 2022 03:58:38 GMT
• Title: Probabilistic Deduction: an Approach to Probabilistic Structured Argumentation
• Authors: Xiuyi Fan
• Abstract summary: 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.
• Score: 1.027974860479791
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces Probabilistic Deduction (PD) as an approach to probabilistic structured argumentation. A PD framework is composed of probabilistic rules (p-rules). As rules in classical structured argumentation frameworks, p-rules form deduction systems. In addition, p-rules also represent conditional probabilities that define joint probability distributions. With PD frameworks, one performs probabilistic reasoning by solving Rule-Probabilistic Satisfiability. At the same time, one can obtain an argumentative reading to the probabilistic reasoning with arguments and attacks. In this work, we introduce a probabilistic version of the Closed-World Assumption (P-CWA) and prove that our probabilistic approach coincides with the complete extension in classical argumentation under P-CWA and with maximum entropy reasoning. We present several approaches to compute the joint probability distribution from p-rules for achieving a practical proof theory for PD. 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.

Related papers

• Understanding ProbLog as Probabilistic Argumentation [0.0]
  We show that ProbLog is an instance of a form of Probabilistic Abstract Argumentation (PAA) that builds upon Assumption-Based Argumentation (ABA) The connections pave the way towards equipping ProbLog with alternative semantics.
  arXiv  Detail & Related papers  (2023-08-30T09:05:32Z)
• Connecting classical finite exchangeability to quantum theory [69.62715388742298]
  Exchangeability is a fundamental concept in probability theory and statistics. We show how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• smProbLog: Stable Model Semantics in ProbLog for Probabilistic Argumentation [19.46250467634934]
  We show that the programs representing probabilistic argumentation frameworks do not satisfy a common assumption in probabilistic logic programming (PLP) semantics. The second contribution is then a novel PLP semantics for programs where a choice of probabilistic facts does not uniquely determine the truth assignment of the logical atoms. The third contribution is the implementation of a PLP system supporting this semantics: smProbLog.
  arXiv  Detail & Related papers  (2023-04-03T10:59:25Z)
• Machine Learning with Probabilistic Law Discovery: A Concise Introduction [77.34726150561087]
  Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. PLD is close to Decision Tree/Random Forest methods, but it differs significantly in how relevant rules are defined. This paper outlines the main principles of PLD, highlight its benefits and limitations and provide some application guidelines.
  arXiv  Detail & Related papers  (2022-12-22T17:40:13Z)
• Probabilistic Conformal Prediction Using Conditional Random Samples [73.26753677005331]
  PCP is a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. It is efficient and compatible with either explicit or implicit conditional generative models.
  arXiv  Detail & Related papers  (2022-06-14T03:58:03Z)
• 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)
• Preferential Structures for Comparative Probabilistic Reasoning [2.0646127669654826]
  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.
  arXiv  Detail & Related papers  (2021-04-06T05:00:20Z)
• Probabilistic Generating Circuits [50.98473654244851]
  We propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are not just a theoretical framework that unifies vastly different existing models, but also show huge potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks.
  arXiv  Detail & Related papers  (2021-02-19T07:06:53Z)
• Contextuality scenarios arising from networks of stochastic processes [68.8204255655161]
  An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. We present a different and classical source of contextual empirical models: the interaction among many processes. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
  arXiv  Detail & Related papers  (2020-06-22T16:57:52Z)

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.