# Many-valued Argumentation, Conditionals and a Probabilistic Semantics for Gradual Argumentation

arXiv: https://arxiv.org/abs/2212.07523 · HTML: https://mlsanity.com/paper/2212.07523/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Interpreting Neural Networks as Gradual Argumentation Frameworks (Including Proof Appendix)](https://mlsanity.com/paper/2012.05738/) (2020)
- [Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs](https://mlsanity.com/paper/1807.06685/) (2018)
- [Epistemic Graphs for Representing and Reasoning with Positive and Negative Influences of Arguments](https://mlsanity.com/paper/1802.07489/) (2018)
- [Weighted defeasible knowledge bases and a multipreference semantics for a deep neural network model](https://mlsanity.com/paper/2012.13421/) (2020)
- [On Rational Entailment for Propositional Typicality Logic](https://mlsanity.com/paper/1809.10946/) (2018)
- [On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach](https://mlsanity.com/paper/2008.02550/) (2020)
- [A conditional, a fuzzy and a probabilistic interpretation of self-organising maps](https://mlsanity.com/paper/2103.06854/) (2021)
- [Boolean algebras of conditionals, probability and logic](https://mlsanity.com/paper/2006.04673/) (2020)
- [An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge bases](https://mlsanity.com/paper/2202.01123/) (2022)

## Built on by (most cited first, 1 of 1)

- [Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality](https://mlsanity.com/paper/2303.04534/) (2023)

## Abstract (arXiv)

In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with respect to a class of gradual semantics, through the verification of graded (strict or defeasible) implications over a preferential interpretation. As a proof of concept, in the finitely-valued case, an Answer set Programming approach is proposed for conditional reasoning in a many-valued argumentation semantics of weighted argumentation graphs. The paper also develops and discusses a probabilistic semantics for gradual argumentation, which builds on the many-valued conditional semantics.