Amgoud and Caminada introduced the ASPIC argumentation theory , proposing a particular instan- tiation of Dung’s abstract argumentation framework , filling the gaps intentionally left unspecified (namely, the internal structure of arguments). In ASPIC , the knowledge base is a pair T = (S, D) of sets of strict and defeasible rules. Arguments are constructed chaining recursively both kinds of rules. Defeat is determined in terms of two kind of attacks: rebuttals (attacks onthe ultimate conclu- sion of an argument), and undercuts (attacks onthe intermediate premises). Finally, the acceptability of these arguments, that is, which arguments survive and which do not, is decided applying one of Dung’s standard semantics. In what follow, we consider whether the four abstract consequence op- erators instantiated accordingly to the ASPIC formalism satisfy cumulativity. Bear in mind that facts in this framework are codified as strict rules with empty body. Thus, the set of facts F is composed by those strict rules with an empty body and the set of rules R is composed by the remaining strict and defeasible rules. Once again, for a given set Q, the operators strict (Q) and defeasible (Q) return, respectively, the strict or defeasible rules in Q.
The study and development of argumentative frameworks has deserved special atten- tion in this regard, since argumentation constitutes a con°uence point for characterizing traditional approaches to non-monotonic reasoning systems, such as Gelfond's extended logic programming and Reiter's default logic [BDKT97]. In that context, Labeled Deduc- tive Systems (LDS) [Gab96] emerged as an interesting alternative that provides a °exible methodology to formalize complex logical systems.
In this research line we are exploring the possibility of having multiple preference criteria to compare arguments ininDefeasibleArgumentation. In this work we are assuming a goal- oriented Argumentative System, to which an application or an agent may seek an answer in response to a query. Thus, based onthe current knowledge available, the system will decide whether there exists undefeated support for that query.
Modeling the epistemic state of a rational agent is the most difficult enterprise that must be addressed in its design process. Pereira et al. have endorsed the use of Extended Logic Programming (ELP) for accomplishing this task . In this setting, the knowledge ofthe agent is codified by a logic program extended with explicit negation, and its beliefs are set by the well-founded semantics of this program. This approach has a clear advantage: it admits a seamless transition between theory and practice. Nevertheless, ELP cannot deal with incomplete and potentially contradictory information, an essential capability in practical agents. Several argumentation formalisms [12,10,8,4,13] have been proposed as knowledge representation and reasoning tools able to handle uncertain information. This property elicits argument-based theories as proper tools for modeling the epistemic state of rational agents. Unfortunately, argumentative systems lack the implementability of ELP.
The growing success ofargumentation-based approaches has caused a rich crossbreeding with other disciplines, providing interesting results in different areas such as legal reasoning, medical diagnosis and decision support systems. Many of these approaches rely on quantita- tive aspects (such as numeric attributes, probabilities or certainty values). As argumentation provides mostly a non-numerical, qualitative setting for commonsense reasoning, integrat- ing both quantitative and qualitative features has shown to be highly desirable [TP01]. Remarkably, numerical reasoning has been long neglected inthedefeasibleargumentation community. This is maybe due to the historical origins ofthe discipline, which were more related to legal (qualitative) reasoning rather than to number-based attributes as those used in rule-based production systems.
• The process that occurs inside an agent reasoning in an argumentative fashion shares the same structure of a dialog between opposing parties analyzing the acceptability of an assertion. We intend to elicit a model for the process of deliberation beginning by formulating a model for the dialectical notions involved in all the formalizations ofdefeasibleargumentation, and then reinterpreting it as a model ofthe deliberation process. Clearly, we rest on Rescher's isomorphism to ensure the feasibility of this approach. Note that the model obtained through this design will be abstract in nature, since it has to capture all the shades of dialectics present inthecontextofthe theories ofdefeasibleargumentation. Nonetheless, this outcome is welcomed since it goes along with our objective of covering a large domain of application.
When introducing numerical values for modeling uncertainty, extensional and inten- sional approaches can be distinguished. Extensional approaches treat uncertainty as a generalized truth value attached to formulas. Computing the uncertainty of any formula is a function ofthe uncertainties of its subformulas. Intensional approaches, onthe other hand, are model-based: uncertainty is attached to \states of a®airs" or subsets of \possi- ble worlds". Typical examples of this extensional approaches are production systems and rule-based systems.
an attractive approach to formalizing complex logical systems, since they allow to characterize the different components involved by using different sorts of labels. One ofthe motivations for developing this framework was namely the definition of a single, unified ontology to capture the main issues involved indefeasibleargumentation by specifying a suitable underlying logical language and its associated inference rules.
Given an argument A:h derivable from a theory ¡ , there may be other con°icting arguments also supported by ¡ which defeat it according to some preference criterion. A common syntactic preference criterion is speci¯city [SL92], which prefers those arguments which are more informed or more `direct'. However, any partial order onthe set of all possible arguments could be used. Since defeaters are arguments, they may be on its turn defeated, and so on. This leads to a recursive analysis, in which a tree structure rooted in A:h results. If A:h ultimately prevails over other con°icting arguments, then A:h is called a warrant. In LDS ar , this situation is formalized in terms of an inference relationship j» T .
In DeLP, a literal h is warranted if there exists a non-defeated argument A supporting h. An argument structure A for a literal h (denoted A, h) is a minimal and consistent set ofdefeasible rules that allows to infer h. In order to establish whether A, h is a non-defeated argument, argument rebuttals or counter-arguments that could be defeaters for A, h are considered, i.e., counter-arguments that by some criterion, are preferred to A, h. Since counter-arguments are arguments, there may exist defeaters for them, and defeaters for these defeaters, and so on. Thus, a sequence of arguments called ar- gumentation line may appear, where each argument defeats its predecessor inthe line (see the following example). Usually, each argument has more than one defeater and more than one argumentation line exists. Therefore, a tree of arguments called dialectical tree is constructed, where the root is A, h and each path from the root to a leaf is an argumentation line. A dialectical analysis of this tree is used for deciding whether h is warranted.
Domain Data Holder (DDH) Domain Data Holder is a masive, potencially contradictory set of domain related data which is used for founding grounds inthe argument building process. Inthe current version ofthe framework, the data is stored in independent relational databases which are accesed via an Open DataBase Connectivity (ODBC) driver, allowing databases to be in any DataBase Management System (DBMS) that has its ODBC driver implemented, like MySQL, SQLite or dBASE. Every database inthe DDH has to be set up with its own ODBC connection before it can be used by the DBI-DeLP server. There isn’t a theoretical limit inthe number of databases included inthe DDH, and the addition or remove of a database has no effect onthe others (but obviosly the knowledge is altered so if a previous query is launched again the answer obtained may vary). Also there aren’t restrictions about how tables and fields should be named, or how the database schema should be, but configuration for each database is needed so the server knows what tables and fields to include inthe SQL query it sends to the DBMS. Nonetheless configuration is as simple as adding rows to tables in a database that keeps information about relations between predicates and databases inthe DDH.
In this context, our research work is oriented towards a formalization of argument-based interaction in electronic institutions by applying different logical models for defeasibleargumentation. Formalizing complex social structures in these institutions is crucial for a complete understanding of many features, such as hierarchies between agents, temporal constraints, computation with limited resources, etc. Such a model would allow to study and analyze the emerging behavior of intelligent, autonomous agents which may interact asynchronously with each other. A useful formalization tool is provided by so-called context-based reasoning, which will be briefly discussed inthe next section.
Defeasibleargumentation has evolved inthe last decade as a successful approach to formalize de- feasible reasoning . The growing success ofargumentation-based approaches has caused a rich crossbreeding with other disciplines, providing interesting results in different areas such as knowl- edge engineering, multiagent systems, and decision support systems, among others [15, 6]. Defea- sible logic programming (DeLP)  is a particular formalization ofdefeasibleargumentation based on logic programming, which has proven to be particularly attractive inthecontextof real-world applications, such as clustering , intelligent web search , knowledge management , natural language processing , and web form-based applications . To make this paper self-contained, we will summarize next the fundamentals of DeLP. 4
Although the World Wide Web is a vast repository of information, its utility is restricted by limited facilities for searching and integrating different kinds of data, as search for queries is mostly syntax- based (e.g., using keywords). The Semantic Web  has emerged as a project intended to create a universal medium for information exchange by giving semantics to the content of documents onthe Web. A common way to provide semantics to documents onthe web is through the use of ontology definitions. Common problems from common-sense reasoning (e.g., reasoning with uncertainty or with incomplete and potentially inconsistent information) are present when defining ontologies. In recent years, defeasibleargumentation has succeeded as approach to formalize such common-sense reasoning [6, 16]. In this preliminary report, we explore different alternatives for defining an ontology algebra whose semantics is based ondefeasibleargumentation and belief revision. We suggest how different aspects of ontology integration can be defined in terms ofdefeasibleargumentation and belief revision.
Later on, H. Prakken drove Loui’s work in single-agent dialectical reasoning into what he calls dynamic multiagent debates . He proposed a somewhat messy model of dialectical argumentationin accord to Loui’s designs. Following an strategy similar to our’s, he then rein- terpreted his model as a model of multiagent interaction. It should be noted that Prakken’s goal was to allow the agents taking part in a debate to dynamically modify their knowledge bases. In contrast, our model concerns only with static debates. We strongly believe further experimentation on static multiagent deliberation is required before exploring these more in- volved scenarios. Unfortunately, Prakken’s proposal falls short of expectations. Like Rescher, he also assumed that all the intervening parties inthe debate share the same knowledge base. This natural assumption inthe single agent scenario becomes unsustainable inthecontextof a multiagent system.
This article addresses the problem of having a robot that must reach a certain goal by means of a given set of actions. In order to achieve this, other problems must be solved first, from the construction ofthe robots to knowledge representation. Here, our main concern will be modelling the software agents that drive the physical robots. We have chosen the BDI ar- chitecture [9, 10], which is “...one ofthe most promising architectures for the development of intelligent agents, and has become one ofthe most studied and well known inthe literature” . Inthe BDI model, reasoning about beliefs, desires and intentions must be performed; we will use Defeasible Logic Programming (DeLP)  as the reasoning module. DeLP is an argumen- tative formalism [1, 8] that relies on a defeasible logic program. In our work, this program will contain rules that combine desires and beliefs to provide the agent with the capability of deriv- ing intentions. Then, when the current intention is determined, the robot will use its eﬀectors to perform the physical action that best accomplishes what the software agent intended.
Unfortunately, the algorithms underlying regular recommender systems are not directly transferable to the area of TEL (Verbert, 2011). These algorithms use information about users and resources to generate recommendations. Purposely, most TEL recommender systems rely on users’ profiles to gather additional information, as opposed to traditional recommenders, that focus on users’ likes or interests. The knowledge level ofthe learner is often used to personalize recommendations, such as his/her knowledge of course concepts or past academic grades. Due to the fact that learning process usually takes place in a notably complex and heterogeneous environments, the use of contextual information relating to the user by recommenders has attracted major interest. Such contextualization is being researched as a paradigm for building intelligent systems that can better predict and anticipate the needs of users, and act more efficiently in response to their behavior (Verbert, 2011).
3. The specific subject matter conditions the choice of frames. The diffe - rences in both subjects explain much ofthe divergence among the frames em - ployed: the dramatic and emotional character ofthe eviction phenomenon determines that the human interest frame be predominant, while with the ‘Wert law’, an issue that has a more conceptual character, everything revolves around the rational speculation onthe causes and the consequences ofthe educa- tional reform. Nevertheless, the development ofthe information on both sub- jects possesses different patterns: while the eviction case generated frequent new information, of dramatic character, and with a strong narrative compo- nent (suicides, protests…), the ‘Wert law’, due to its static character, was upda - ted to a lesser degree by the media, which did not give rise to new reports that could open the interpretative spectrum. Due to these reasons, the predominant frames used were different. Most ofthe participants ofthe debate evaluated the eviction phenomenon from the same frames. The coincidence that the data show when framing the eviction phenomenon is explained, in part, by the spe- cific subject matter ofthe evictions that, as already pointed out, possessed a dramatic character, and therefore, was markedly emotional. There isn’t much interpretative unanimity inthe case ofthe ‘Wert law’. In this issue, a greater diversification ofthe frames assigned to the different profiles is observed.
Among them: the development of methods to reduce the risks of losses using SDR by states, taking into account the criticism of countries inthe absence of their provision. It is intended to interest the private sector in their application in transactions in order to expand the demand for the functioning of this international currency unit, which is actually used inthe limited official sphere ofthe Fund’s relations with the central banks of member countries. The idea of issuing bonds nominated in SDR, and even more so the creation of an international market for such bonds, is difficult to implement, since the competitive market of bonds, nominated in real world currencies - the US dollar, euro and other currencies that are in demand, is active.