A computational method for defeasible argumentation based on a recursive warrant semantics

Abstract. In a recent pape

RP-DeLP: a weighted defeasible argumentation framework based on a recursive semantics

In this paper we first define a recursive semantics for warranted formulas in a general defeasible argumentation framework by formalizing a notion of collective (non-binary) conflict among arguments. The recursive semantics for warranted formulas is based on the fact that if the argument is rejected, then all arguments built on it should also be rejected. The main characteristic of our recursive semantics is that an output (extension) of a knowledge base is a pair of sets of warranted and blocked formulas. Arguments for both warranted and blocked formulas are recursively based on warranted formulas but, while warranted formulas do not generate any collective conflict, blocked conclusions do. Formulas that are neither warranted nor blocked correspond to rejected formulas. Second we extend the general defeasible argumentation framework by attaching levels of preference to defeasible knowledge items and by providing a level-wise definition of warranted and blocked formulas. Third we formalize the warrant recursive semantics for the particular framework of Possibilistic Defeasible Logic Programming, we call this particular framework Recursive Possibilistic Defeasible Logic Programming (\mbox{RP-DeLP} for short), and we show its relevance in the scope of Political debates. An RP-DeLP program may have multiple outputs in case of circular definitions of conflicts among arguments. So, we tackle the problem of which output one should consider for an RP-DeLP program with multiple outputs. To this end we define the maximal ideal output of an RP-DeLP program as the set of conclusions which are ultimately warranted and we present an algorithm for computing them in polynomial space and with an upper bound on complexity equal to P^{NP}. Finally, we propose an efficient and scalable implementation of this algorithm that is based on implementing the two main queries of the system, looking for valid arguments and collective conflicts between arguments, using SAT encodings. We perform an experimental evaluation of our SAT based approach when solving test sets of instances with single and multiple preference levels for defeasible knowledge.The authors are very thankful to the anonymous reviewers for their helpful and constructive comments. This research was partially supported by the Spanish projects ARINF (TIN2009- 14704-C03-01), TASSAT (TIN2010-20967-C04-03), EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)

Algorithms and efficient encodings for argumentation frameworks and arithmetic problems

In this thesis we focus on the design and implementation of a particular framework of Possibilistic Defeasible Logic Programming (RP-DeLP). This framework is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. An output of an RP-DeLP program is a pair of sets of warranted and blocked conclusions (literals), all of them recursively based on warranted conclusions but, while warranted conclusions do not generate any conflict, blocked conclusions do. An RP-DeLP program may have multiple outputs in case of circular definitions of conflicts among arguments. We introduce two semantics, the first one where all possible outputs are computed and the second one which is a characterization of an unique output property. The computation of the outputs for both semantics relies on two main problems: the problem of finding a collective conflict among a set of arguments and the problem of finding almost valid arguments for a conclusion. Both problems are combinatorial problems, so we propose two resolution approaches: a first one based on SAT techniques and a second one based on Answer Set Programming techniques. We propose an implementation and we empirically test our algorithms. We provide an analysis on the performance of the implementation of the algorithms, and we explain the results on the resolution of some randomly generated problems. In this thesis we also focus on the resolution of some combinatorial problems. We analyze, design and implement some resolution tools for arithmetic problems, modular constraints and networking problems. We studied empirically how our approaches perform and we compared them to other solving techniques known as best proposals in the literature.Esta tesis se centra en el diseño e implementación de un framework particular para Possibilistic Defeasible Logic Programming (RP-DeLP). Este framework está basado en la noción general de conflicto colectivo entre argumentos (no binario) que permite asegurar las propiedades de consistencia directa e indirecta respecto al conocimiento estricto. Una salida de un programa RP-DeLP es una tupla de conjuntos de conclusiones (literales) garantizadas y bloqueadas, todas ellas basadas recursivamente sobre conclusiones garantizadas con la particularidad de que mientras las conclusiones garantizadas no generan ningún conflicto, las conclusiones bloqueadas sí lo hacen. Un programa RP-DeLP puede tener múltiples salidas en el caso de que existan definiciones circulares de conflictos entre los argumentos. Se introducen dos semánticas, la primera donde se computan todas las posibles salidas del programa y una segunda que nace de la caracterización de la propiedad de la salida única. El cómputo de las salidas para ambas semánticas se basa en la solución de dos problemas principales: el problema de la búsqueda de argumentos almost valid para una conclusión y la búsqueda de conflictos colectivos entre un conjunto de argumentos. Ambos problemas son problemas combinatorios y se proponen dos aproximaciones de resolución diferentes: una primera aproximación basada en técnicas SAT y otra segunda aproximación basada en técnicas de Answer Set Programming. Se propone una implementación y también se prueba empíricamente el comportamiento de los algoritmos propuestos. A través de un análisis sobre el comportamiento de la implementación se explican los resultados obtenidos. Para ello se generan problemas aleatorios donde algunas propiedades pueden ser controladas mediante la configuración de parámetros de entrada. Adicionalmente esta tesis también se centra en la resolución de otros problemas combinatorios. Se analizan e implementan herramientas para la resolución de problemas aritméticos, restricciones modulares y problemas de redes de comunicaciones. Se propone un estudio empírico de las propuestas y se comparan con las aproximaciones, conocidas como más eficientes hasta el momento, de la literatura.Aquesta tesi doctoral se centra en el disseny i implementació d'un framework particular per Possibilistic Defeasible Logic Programming (RP-DeLP). Aquest framework es basa en una noció de conflicte col·lectiu (no binària) entre arguments que permet assegurar les propietats de consistència directa i indirecta respecte del coneixement estricte. Una sortida d'un programa RP-DeLP és una parella de conjunts de conclusions garantides i bloquejades (literals), totes elles basades recursivament en conclusions prèviament garantides. La diferència radica en què mentre les conclusions garantides no generen cap conflicte, les conclusions bloquejades sí que ho fan. Un programa RP-DeLP pot tenir múltiples sortides en el cas de definicions circulars de conflictes entre arguments. S'introdueixen dues semàntiques pel sistema d'argumentació presentat. La primera d'elles pren en consideració totes les possibles sortides que poden ser obtingudes d'un programa RP-DeLP tenint en compte les diferents maneres de resoldre els conflictes circulars que poden sorgir. La segona semàntica se centra en el còmput d'una única sortida que està basada en la caracterització del que anomenem maximal ideal output. Aquesta sortida conté un nombre maximal de literals garantits, però que inclou només literals els arguments dels quals tenen els seus suports inclosos en la sortida. El comput de les sortides per ambdues semàntiques es basa en la resolució de dos problemes principals: el problema de trobar conflictes col·lectius entre un conjunt d'arguments i el problema de trobar arguments almost valid per una conclusió. Ambdós problemes són considerats problemes combinatoris i es proposen dues aproximacions per a la resolució: una primera aproximació basada en tècniques SAT i una segona basada en Answer Set Programming. Es proposa una implementació i una anàlisi empírica dels algorismes implementats. Aquests algorismes es proven sobre un conjunt de problemes generats aleatòriament mitjançant un generador que permet la configuració dels diferents paràmetres dels problemes generats. Un cop obtinguts els resultats, s'estudia quina afectació han tingut els diferents paràmetres observant el temps de resolució i la informació obtinguda. En aquesta tesi també s'estudien diferents tècniques de resolució per a altres problemes combinatoris. S'analitzen, dissenyen i implementen algunes eines de resolució per a problemes aritmètics, restriccions modulars i problemes de xarxes de comunicacions. S'ha estudiat com les aproximacions proposades es comporten en comparació amb altres tècniques proposades a la literatura considerades com les més eficients fins al moment

A logic of defeasible argumentation: Constructing arguments in justification logic

In the 1980s, Pollock’s work on default reasons started the quest in the AI community for a formal system of defeasible argumentation. The main goal of this paper is to provide a logic of structured defeasible arguments using the language of justification logic. In this logic, we introduce defeasible justification assertions of the type t:F that read as “t is a defeasible reason that justifies F”. Such formulas are then interpreted as arguments and their acceptance semantics is given in analogy to Dung’s abstract argumentation framework semantics. We show that a large subclass of Dung’s frameworks that we call “warranted” frameworks is a special case of our logic in the sense that (1) Dung’s frameworks can be obtained from justification logic-based theories by focusing on a single aspect of attacks among justification logic arguments and (2) Dung’s warranted frameworks always have multiple justification logic instantiations called “realizations”. We first define a new justification logic that relies on operational semantics for default logic. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons or pieces of evidence that might conflict with one another. To amend this, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. This enables us to formalize non-monotonic justifications that prompt extension revision already for normal default theories. Then we present our logic as a system for abstract argumentation with structured arguments. The format of conflicting reasons overlaps with the idea of attacks between arguments to the extent that it is possible to define all the standard notions of argumentation framework extensions. Using the definitions of extensions, we establish formal correspondence between Dung’s original argumentation semantics and our operational semantics for default theories. One of the results shows that the notorious attack cycles from abstract argumentation cannot always be realized as justification logic default theories

Automata for infinite argumentation structures

The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this limitation, in this paper we propose a novel approach for describing infinite afs using tools from formal language theory. In particular, the possibly infinite set of arguments is specified through the language recognized by a deterministic finite automaton while a suitable formalism, called attack expression, is introduced to describe the relation of attack between arguments. The proposed approach is shown to satisfy some desirable properties which cannot be achieved through other “naive” uses of formal languages. In particular, the approach is shown to be expressive enough to capture (besides any arbitrary finite structure) a large variety of infinite afs including two major examples from previous literature and two sample cases from the domains of multi-agent negotiation and ambient intelligence. On the computational side, we show that several decision and construction problems which are known to be polynomial time solvable in finite afs are decidable in the context of the proposed formalism and we provide the relevant algorithms. Moreover we obtain additional results concerning the case of finitaryafs

Evaluating the Impact of Defeasible Argumentation as a Modelling Technique for Reasoning under Uncertainty

Limited work exists for the comparison across distinct knowledge-based approaches in Artificial Intelligence (AI) for non-monotonic reasoning, and in particular for the examination of their inferential and explanatory capacity. Non-monotonicity, or defeasibility, allows the retraction of a conclusion in the light of new information. It is a similar pattern to human reasoning, which draws conclusions in the absence of information, but allows them to be corrected once new pieces of evidence arise. Thus, this thesis focuses on a comparison of three approaches in AI for implementation of non-monotonic reasoning models of inference, namely: expert systems, fuzzy reasoning and defeasible argumentation. Three applications from the fields of decision-making in healthcare and knowledge representation and reasoning were selected from real-world contexts for evaluation: human mental workload modelling, computational trust modelling, and mortality occurrence modelling with biomarkers. The link between these applications comes from their presumptively non-monotonic nature. They present incomplete, ambiguous and retractable pieces of evidence. Hence, reasoning applied to them is likely suitable for being modelled by non-monotonic reasoning systems. An experiment was performed by exploiting six deductive knowledge bases produced with the aid of domain experts. These were coded into models built upon the selected reasoning approaches and were subsequently elicited with real-world data. The numerical inferences produced by these models were analysed according to common metrics of evaluation for each field of application. For the examination of explanatory capacity, properties such as understandability, extensibility, and post-hoc interpretability were meticulously described and qualitatively compared. Findings suggest that the variance of the inferences produced by expert systems and fuzzy reasoning models was higher, highlighting poor stability. In contrast, the variance of argument-based models was lower, showing a superior stability of its inferences across different system configurations. In addition, when compared in a context with large amounts of conflicting information, defeasible argumentation exhibited a stronger potential for conflict resolution, while presenting robust inferences. An in-depth discussion of the explanatory capacity showed how defeasible argumentation can lead to the construction of non-monotonic models with appealing properties of explainability, compared to those built with expert systems and fuzzy reasoning. The originality of this research lies in the quantification of the impact of defeasible argumentation. It illustrates the construction of an extensive number of non-monotonic reasoning models through a modular design. In addition, it exemplifies how these models can be exploited for performing non-monotonic reasoning and producing quantitative inferences in real-world applications. It contributes to the field of non-monotonic reasoning by situating defeasible argumentation among similar approaches through a novel empirical comparison