Paretian argumentation frameworks for Pareto optimal arguments

The Attack-Support Argumentation Framework (ASAF) is an abstract argumentation framework that provides a unified setting for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level. Currently, the extensions of the ASAF are obtained by translating it into a Dung's Argumentation Framework (AF). In this work we provide the ASAF with the ability of determining its extensions without requiring such a translation. We follow an extension-based approach for characterizing the acceptability semantics directly on the ASAF, considering the complete, preferred, stable and grounded semantics. Finally, we show that the proposed characterization satisfies different results from Dung's argumentation theory.

Credulous acceptance in high-order argumentation frameworks with necessities: An incremental approach

Dung's argumentation framework is an abstract framework based on a set of arguments and a binary attack relation defined over the set. One instantiation, among many others, of Dung's framework consists in constructing the arguments from a set of propositional logic formulas. Thus an argument is seen as a reason for or against the truth of a particular statement. Despite its advantages, the argumentation approach for inconsistency handling also has important shortcomings. More precisely, in some applications what one is interested in are not so much only the conclusions supported by the arguments but also the precise explications of such conclusions. We show that argumentation framework applied to classical logic formulas is not suitable to deal with this problem. On the other hand, intuitionistic logic appears to be a natural alternative candidate logic (instead of classical logic) to instantiate Dung's framework. We develop constructive argumentation framework. We show that intuitionistic logic offers nice and desirable properties of the arguments. We also provide a characterization of the arguments in this setting in terms of minimal inconsistent subsets when intuitionistic logic is embedded in the modal logic S4.

We propose a logical encoding of extended abstract argumentation frameworks, that is frameworks with higher-order attacks (i.e. attacks whose targets are other attacks). Our purpose is to separate the logical expression of the meaning of an attack (simple or higher-order) from the logical expression of acceptability semantics. We consider semantics which specify the conditions under which the arguments (resp. the attacks) are considered as accepted, directly on the extended framework, without translating the original framework into a Dung's argumentation framework. We characterize the output of a given framework in logical terms (namely as particular models of a logical theory). Our proposal applies to the particular case of Dung's frameworks, enabling to recover standard extensions.

The system ASPARTIX is a tool for computing acceptable extensions for a broad range of formalizations of Dung's argumentation framework and generalizations thereof. ASPARTIX relies on a fixed disjunctive datalog program which takes an instance of an argumentation framework as input, and uses the answer-set solver DLV for computing the type of extension specified by the user.

Argumentative reasoning and taxonomic analysis for the identification of medical errors

This paper reconsiders Modgil's Extended Argumentation Frameworks EAFs that extend Dung's abstract argumentation frameworks by attacks on attacks. This allows to encode preferences directly in the framework and thus also to reason about the preferences themselves. As a first step to reduction-based approaches to implement EAFs, we give an alternative but equivalent characterization of acceptance in EAFs. Then we use this characterization to provide EAF encodings for answer set programming and propositional logic. Moreover, we address an open complexity question and the expressiveness of EAFs.

An abstract framework for structured arguments is presented, which instantiates Dung's (‘On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n-Person Games’, Artificial Intelligence, 77, 321–357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog.

In this paper we propose a labelling based dialogue game for determining whether a single argument within a Dung argumentation framework is skeptically preferred. Our game consists of two phases, and determines the membership of a single argument within the extension, assuming optimal play by dialogue participants. In the first phase, one player attempts to advance arguments to construct an extension not containing the argument under consideration, while the second phase verifies that the extension is indeed a preferred one. Correctness within this basic game requires perfect play by both players, and we therefore also introduce an overarching game to overcome this limitation.

The article is devoted to the contribution of the prominent Italian economist Vilfredo Pareto to the theory of public welfare. The main theoretical achievements of the economist regarding the definition and measurement of public welfare are highlighted. Vilfredo Pareto rejected the principle of quantitative utility and developed his own concept of welfare maximization through the theory of such an optimal distribution of resources, including goods, in which any redistribution of them will not lead to an increase in the utility of an individual without a decrease in utility for other individuals. Giving decisive importance to the effective distribution of resources as opposed to their endless maximization, V. Pareto noted for the first time in the many years of development of economic thought that the sources of social well-being cannot be considered solely enrichment with material goods, since the possibility of their effective redistribution on the basis of humanity and high moral and ethical values. That is, for the first time in the theory of well-being, the level of human development of society, its moral values, and the weight of ethical and humanistic principles become important. These approaches make it possible to determine a relative criterion for the efficiency (optimality) of the functioning of the economic system, which specifies the state of optimality according to the following principle: it is the achievement of such a state when no one can improve their situation without getting worse. The importance of determining the optimum from the point of view of production is indicated. At the same time, we are talking about the structure of production with a certain amount of resources and technical support, which, according to his approach, becomes optimal when it is impossible to increase the production of one product without simultaneously reducing production. Such an optimal situation occurs when the marginal productivity of production factors is the same in all variants of their application. An analysis was made of provisions where the growth of social welfare does not concern the volume of production or resources, but the consumption of materials and the creation of aggregate social demand. Since, according to the terminology, gross output and gross income of the country are one and the same (the estimate of production volumes is equal to the sum of payments to the owners of input resources), the "Pareto Optimum" is the maximum production (or income) of the economy and is the most effective operational indicator. From the perspective of political decision-making, the idea of the "Pareto optimum" leads to the following Pareto criterion for the formulation of political goals: a change in social policy is justified if, as a result of such a change, all members of society will be better off, or if the improvement will affect some of its members and the condition of all others will not deteriorate. This distribution of goods in an economy is otherwise efficient when they cannot be redistributed to improve the position of one member of society without simultaneously worsening the position of another member of society. Based on this, the quality of life should become a consolidating idea in Ukraine, which will enable the nation to build its own path of development, in which ensuring the conditions for the successful realization of the individual will become the main way for evaluating the effectiveness of economic reforms

In this paper we further progress the analysis of the recently introduced multi-valued argumentation frameworks (MVAFs). MVAFs are an extension of Dung's abstract argumentation, where arguments have a degree of truth associated with them. Here we describe a list of properties of MVAFs considering the major multi-valued logics such as those proposed by Gödel, Zadeh and Łukasiewicz. We then propose a computational framework that joins multi-valued and probabilistic argumentation frameworks to handle situations where arguments affected by vagueness and/or probabilities coexist. The findings are a contribution to the field of non-monotonic approximate reasoning and they also represent a well-grounded proposal towards the introduction of gradualism in argumentation systems.

We study the problem of fair allocation of items / goods / resources to m agents. The problem appears in two broad variants: (a) fair allocation of a divisible item wherein one item is to be divided amongst m agents; the problem is popularly known as cake-cutting problem, (b) fair allocation of indivisible items wherein n indivisible or non-shareable items are to be allocated amongst m agents. Further, the item/items can be homogeneous or heterogeneous. Both the variants have several real-time applications such as land-division amongst heirs is an example of allocation of a divisible item, whereas in divorce settlement, division of assets such as house, car, artifacts, etc. is an example of allocation of indivisible items. There are many notions of fairness and social welfare that are important and have been studied: envy-freeness, proportionality, Pareto optimality, maximin share guarantee, Borda maximin share guarantee, utilitarian social welfare, egalitarian social welfare and Nash social welfare. In this chapter, we discuss about the fair-allocation problem and their related results.

We study the optimal allocation of heterogeneous services without using monetary transfers. Agents have private, multi-dimensional utilities over the services, and a social planner has arbitrary priors on the utilities, which may depend on the agents' observable characteristics. The social planner's goal is to maximize a public objective, which may be complex, taking into account diverse considerations such as social welfare, equity, and system costs. Potential applications include the allocation of seats to public schools, spaces in college dorms or courses, and spots in subsidized housing. We propose an engineering approach to such problems, in which we simplify the analysis by considering a large-market model with a continuum of agents, and show using real data that a mechanism defined based on this approximation still yields good results in the finite market. In the large-market model, there are finitely many types, and a continuum of agents of each type. (Here, corresponds to an agent's observable information, which is distinct from the private utilities.) The large market assumption implies that a mechanism can be decomposed into a collection of allocation rules, one for each type. We show that any allocation rule that satisfies incentive compatibility and Pareto optimality within type is representable as Competitive Equilibrium with Equal Incomes (CEEI). In other words, for each type of agents and for each service, there exists a virtual price for a unit of probability of getting that service, and the allocation is induced by giving each agent one unit of virtual money' and having them purchase their utility-maximizing probabilities to services. In addition, if the mechanism is restricted to being 'ordinal,' which means that it only uses preference rankings but not preference intensities, then an allocation rule that satisfies incentive compatibility and ordinal efficiency within type is 'lottery-plus-cutoff': each agent receives a uniformly random lottery number between zero and one, and for each service and each type, there is a 'lottery cutoff'; an agent is 'admitted' to a service if her lottery number is below the cutoff; each agent is allocated her most preferred service for which she is admitted. Such characterization results reduce the search of the optimal mechanism to a well-defined optimization over the prices and cutoffs for each type. We show how this large market approximation can be applied to an empirically relevant finite setting and yield good results. We consider the allocation of seats in public schools in Boston, which was a real problem faced by a city committee in the 2012-2013 Boston school assignment reform. Students are classified into 868 types by home location and there is a utility model for each type that comes from fitting a multinomial logit discrete choice model on previous years' data. There are 77 elementary schools with given capacities. Depending on their home location, a student is given a menu of options and can submit a preference ranking over the schools in the menu. Given preference submissions, a centralized algorithm computes the assignment using a system of priorities, possibly randomizing to break ties. The goal is to optimize the menus and priorities to maximize a weighted combination of social welfare and max-min welfare, while staying within a budget for expected amount of busing needed. Although this is a finite market problem, we can define a large market approximation. Using the characterization results, we show that the optimal mechanism can be encoded as an exponential-sized linear program, which due to the logit utility structure can be efficiently solved using duality theory. Using the cutoffs that arise from this optimization, we define a feasible finite market mechanism that is based on the Deferred Acceptance algorithm. We evaluate the resultant mechanism by simulating in the finite market setting with real data, and show that compared to the mechanism chosen by the city, this new mechanism significantly improves simultaneously in social welfare, max-min welfare and predictability, while staying within the same expected busing budget. In sum, we incorporate prior information in the allocation problem without monetary transfers, and exhibit computational results in empirically relevant special cases.

Welfare economics is the study of decision‐making with the aim of enhancing social welfare, in contrast to an individual's happiness or a firm's profit. This subject should be of value to government (since government is meant to be an agency for promoting social welfare); to an individual who is not committed solely to enhancing his or her own happiness; or even to the “enlightened” firm or business corporation that seeks not only to increase its profit but also has some commitment to the general well‐being of society. Welfare economics has two main concerns: (i) the abstract problem of deciding what constitutes social welfare; and (ii) the more mundane one of deciding how to choose between projects, taxation schemes, industrial regulation, environmental policy, and so on, given some agreed‐upon notion of social welfare. The most influential position has been a utilitarian one – however, it has been criticized. This analysis looks at Vilfredo Pareto's Pareto Optimality and Arrow's impossibility theorem; and it recognizes the place of welfare economics in the economist's repertoire.

Dynamic Efficiency and Pareto Optimality in a Stochastic OLG Model with Production and Social Security