Abstract The unusually warm sea surface temperature events known as marine heatwaves (MHWs) have a profound impact on marine ecosystems. Accurate prediction of extreme MHWs has significant scientific and financial worth. However, existing methods still have certain limitations, especially in the most extreme MHWs. In this study, to address these issues, based on the physical nature of MHWs, we created a novel deep learning neural network that is capable of accurate 10 day MHW forecasting. Our framework significantly improves the forecast ability of extreme MHWs through two specially designed modules inspired by numerical models: a coupler and a probabilistic data argumentation. The coupler simulates the driving effect of atmosphere on MHWs while the probabilistic data argumentation approaches significantly boost the forecast ability of extreme MHWs based on the idea of ensemble forecast. Compared with traditional numerical prediction, our framework has significantly higher accuracy and requires fewer computational resources. What’s more, explainable AI methods show that wind forcing is the primary driver of MHW evolution and reveal its relation with air-sea heat exchange. Overall, our model provides a framework for understanding MHWs’ driving processes and operational forecasts in the future.

Investigation of Semantic Behavior in Probabilistic Argumentation

Abstract The study of Dung-style Argumentation Frameworks in recent years has focused on incorporating time. For example, availability intervals have been added to arguments and relations, resulting in different outputs of Dung semantics over time. This paper examines the probability distribution of arguments over time intervals. Using this temporal probabilistic model, the study explores how these frameworks can be transformed into a probabilistic argumentation according to the constellation approach and how they can be interpreted within the epistemic approach. The epistemic approach relies on the notion of defeat to select significant conflicts based on probability distributions. The study also introduces the temporal acceptability of arguments based on the concept of defence, allowing for more precise results over time. Finally, the models (constellation and epistemic) are extended to account for events that have a duration, i.e. that can occur for several consecutive instants of time.

Probabilistic Argumentation naturally supports the integration of quantitative (probabilistic) reasoning and qualitative argumentation. Meanwhile, Jury-based Probabilistic Argumentation supports the combination of opinions by different reasoners. We show how Jury-based Probabilistic Argumentation (JPAA) and a form of Jury-based Probabilistic Assumption-based Argumentation (JPABA) can naturally support forecasting, whereby subjective probability estimates are combined to make predictions about future events. The form of JPABA we consider is an instance of JPAA and results from integrating Assumption-Based Argumentation (ABA) and probability spaces expressed by Bayesian networks. We show how JPAA and (the considered form of) JPABA can support forecasting by allowing different forecasters to determine the probability of arguments (and, in JPABA, sentences) with respect to their own probability spaces, while sharing arguments (and, in JPABA, their components). We show in turn how this supports the aggregation of individual forecasts into group forecasts.

ProbLog is a popular probabilistic logic programming language/tool, widely used for applications requiring to deal with inherent uncertainties in structured domains. In this paper we study connections between ProbLog and a variant of another well-known formalism combining symbolic reasoning and reasoning under uncertainty, i.e. probabilistic argumentation. Specifically, 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, inherited from PAA/PABA, as well as obtaining novel argumentation semantics for PAA/PABA, leveraging on prior connections between ProbLog and argumentation. Further, the connections pave the way towards novel forms of argumentative explanations for ProbLog's outputs.

Dung's Argumentation Framework (AF) has been extended in several directions, including the possibility of representing uncertainty about the existence of arguments and attacks. In this regard, two main proposals have been introduced in the literature: Probabilistic Argumentation Framework (PrAF) and Incomplete Argumentation Framework (iAF). PrAF is an extension of AF with probability theory, thus representing quantified uncertainty. In contrast, iAF represents unquantified uncertainty, that is it can be seen as a special case where we only know that some elements (arguments or attacks) are uncertain. In this paper, we first address the problem of computing the probability that a given argument is accepted in PrAF. This is carried out by introducing the concept of probabilistic explanation for any given (probabilistic) extension. We show that the complexity of the problem is FP#P-hard and propose polynomial approximation algorithms with bounded additive error for PrAFs where odd-length cycles are forbidden. We investigate the approximate complexity of the related FP#P-hard problems of credulous and skeptical acceptance in PrAF, showing that they are generally harder than the problem of computing the probability that a given argument is accepted. Next we consider iAF and, after showing some equivalence properties among classes of iAFs, we study iAF as a special case of PrAF where uncertain elements have associated a probability equal to 1/2. Finally, given this result, we investigate the relationships between iAF acceptance problems and probabilistic acceptance in PrAF.

Abstract Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modeling tools to account for it. The first contribution of this paper is a novel interpretation of probabilistic argumentation frameworks as probabilistic logic programs. Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. We show that the programs representing probabilistic argumentation frameworks do not satisfy a common assumption in probabilistic logic programming (PLP) semantics, which is, that probabilistic facts fully capture the uncertainty in the domain under investigation. The second contribution of this paper 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 of this paper is the implementation of a PLP system supporting this semantics: smProbLog. smProbLog is a novel PLP framework based on the PLP language ProbLog. smProbLog supports many inference and learning tasks typical of PLP, which, together with our first contribution, provide novel reasoning tools for probabilistic argumentation. We evaluate our approach with experiments analyzing the computational cost of the proposed algorithms and their application to a dataset of argumentation problems.

Human and artificial reasoning has to deal with uncertain environments. Ideally, probabilistic information is available. However, sometimes probabilistic information may not be precise or it is missing entirely. In such cases we reason with higher-order uncertainty. Formal argumentation is one of the leading formal methods to model defeasible reasoning in artificial intelligence, in particular in the tradition of Dung's abstract argumentation. Also from the perspective of cognition, reasoning has been considered as argumentative and social in nature, for instance by Mercier and Sperber. In this paper we use formal argumentation to provide a framework for reasoning with higher-order uncertainty. Our approach builds strongly on Haenni's system of probabilistic argumentation, but enhances it in several ways. First, we integrate it with deductive argumentation, both in terms of the representation of arguments and attacks, and in terms of utilizing abstract argumentation semantics for selecting some out of a set of possibly conflicting arguments. We show how our system can be adjusted to perform well under the so-called rationality postulates of formal argumentation. Second, we provide several notions of argument strength which are studied both meta-theoretically and empirically. In this way the paper contributes a formal model of reasoning with higher-order uncertainty with possible applications in artificial intelligence and human cognition.

The Bipolar Argumentation Framework approach is an extension of the Argumentation Framework. A Bipolar Argumentation Framework considers a support interaction between arguments, besides the attack interaction. As in the Argumentation Framework, some researches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a Bipolar Argumentation Framework under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real application domains there is a need for aggregating probability values from different sources so it is not suitable to aggregate such probability values in a unique probability distribution. To tackle this challenge, we use credal networks theory for modelling the uncertainty of the degree of belief of arguments in a BAF. We also propose an algorithm for calculating the degree of uncertainty of the extensions inferred by a given argumentation semantics. Moreover, we introduce the idea of modelling the support relation as a causal relation. We formally show that the introduced approach is sound and complete w.r.t the credal networks theory.

Evidence from studies, such as in science or medicine, often corresponds to conditional probability statements. Furthermore, evidence can conflict, in particular when coming from multiple studies. Whilst it is natural to make sense of such evidence using arguments, there is a lack of a systematic formalism for representing and reasoning with conditional probability statements in computational argumentation. We address this shortcoming by providing a formalization of conditional probabilistic argumentation based on probabilistic conditional logic. We provide a semantics and a collection of comprehensible inference rules that give different insights into evidence. We show how arguments constructed from proofs and attacks between them can be analyzed as arguments graphs using dialectical semantics and via the epistemic approach to probabilistic argumentation. Our approach allows for a transparent and systematic way of handling uncertainty that often arises in evidence.

From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.

Dung’s Argumentation Framework (AF) has been extended in several directions, including the possibility of representing unquantified uncertainty about the existence of arguments and attacks. The framework resulting from such an extension is called incomplete AF (iAF). In this paper, we first introduce three new satisfaction problems named totality, determinism and functionality, and investigate their computational complexity for both AF and iAF under several semantics. We also investigate the complexity of credulous and skeptical acceptance in iAF under semi-stable semantics—a problem left open in the literature. We then show that any iAF can be rewritten into an equivalent one where either only (unattacked) arguments or only attacks are uncertain. Finally, we relate iAF to probabilistic argumentation framework, where uncertainty is quantified.

Abstract argumentation is a prominent reasoning framework. It comes with a variety of semantics and has lately been enhanced by probabilities to enable a quantitative treatment of argumentation. While admissibility is a fundamental notion for classical reasoning in abstract argumentation frameworks, it has barely been reflected so far in the probabilistic setting. In this paper, we address the quantitative treatment of abstract argumentation based on probabilistic notions of admissibility. Our approach follows the natural idea of defining probabilistic semantics for abstract argumentation by systematically imposing constraints on the joint probability distribution on the sets of arguments, rather than on probabilities of single arguments. As a result, there might be either a uniquely defined distribution satisfying the constraints, but also none, many, or even an infinite number of satisfying distributions are possible. We provide probabilistic semantics corresponding to the classical complete and stable semantics and show how labeling schemes provide a bridge from distributions back to argument labelings. In relation to existing work on probabilistic argumentation, we present a taxonomy of semantic notions. Enabled by the constraint-based approach, standard reasoning problems for probabilistic semantics can be tackled by SMT solvers, as we demonstrate by a proof-of-concept implementation.

Argument strength in probabilistic argumentation based on defeasible rules

Computational complexity of flat and generic Assumption-Based Argumentation, with and without probabilities

Including Probabilistic Uncertainty Into AI-Based Legal Argumentation

A probabilistic deontic argumentation framework

While existing inference engines solved real world problems using probabilistic knowledge representation, one challenging task is to efficiently utilize the representation under a situation of uncertainty during conflict resolution. This paper presents a new approach to straightforwardly combine a rule-based system (RB) with a probabilistic graphical inference framework, i.e., naïve Bayesian network (BN), towards probabilistic argumentation via a so-called probabilistic assumption-based argumentation (PABA) framework. A rule-based system (RB) formalizes its rules into defeasible logic under the assumption-based argumentation (ABA) framework while the Bayesian network (BN) provides probabilistic reasoning. By knowledge integration, while the former provides a solid testbed for inference, the latter helps the former to solve persistent conflicts by setting an acceptance threshold. By experiments, effectiveness of this approach on conflict resolution is shown via an example of liver disorder diagnosis.

In the constellations approach to probabilistic argumentation, there is a probability distribution over the subgraphs of an argument graph, and this can be used to represent the uncertainty in the structure of the argument graph. In this paper, we consider how we can construct this probability distribution from data. We provide a language for data based on perspectives (opinions) on the structure of the graph, and we introduce a framework (based on general properties and some specific proposals) for aggregating these perspectives, and as a result obtaining a probability distribution that best reflects these perspectives. This can be used in applications such as summarizing collections of online reviews and combining conflicting reports.

Cases or examples can be often explained by the interplay of arguments in favour or against their outcomes. This paper addresses the problem of finding explanations for a collection of cases where an explanation is a labelled argumentation graph consistent with the cases, and a case is represented as a statement labelling. The focus is on semi-abstract argumentation graphs specifying attack and subargument relations between arguments, along with particular complete argument labellings taken from probabilistic argumentation where arguments can be excluded. The framework and computational considerations lead to an iterated local iterative deepening depth-first search to collect ‘interesting’ semi-abstract argumentation graphs consistent with a collection of statement labellings. Finally, the framework is illustrated and evaluated with a proof-of-concept implementation.