A Parameterised Hierarchy of Argumentation Semantics for Extended Logic Programming and its Application to the Well-founded Semantics

Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships between the semantics and examine some essential properties concerning consistency and the coherence principle, which relates default negation and explicit negation. Most significantly, we place existing semantics put forward in the literature in our hierarchy and identify a particular argumentation semantics for which we prove equivalence to the paraconsistent well-founded semantics with explicit negation, WFSX$_p$. Finally, we present a general proof theory, based on dialogue trees, and show that it is sound and complete with respect to the argumentation semantics.Comment: To appear in Theory and Practice of Logic Programmin

Distributed knowledge bases : A proposal for argumentation-based semantics with cooperation

O objectivo principal desta dissertação é definir um ambiente de negociação, baseada em argumentação, para bases de conhecimento distribuídas. As bases de conhecimentos são modeladas sobre um ambiente multiagente tal que cada agente possui uma base de conhecimento própria. As bases de conhecimento dos diversos agentes podem ser independentes ou podem incluir conhecimentos comuns. O requisito mínimo para haver negociação num ambiente multiagente é que os agentes tenham a capacidade de fazer propostas, que poderão ser aceites ou rejeitadas. Numa abordagem mais sofisticada, os agentes poderão responder com contra-propostas, com o intuito de alterar aspectos insatisfatórios da pro­ posta original. Um tipo ainda mais elaborado de negociação será o baseado em argumentação. A metáfora da argumentação parece ser adequada à modelação de situações em que os diferentes agentes interagem com o propósito de determinar o significado das crenças comuns. Numa negociação baseada em argumentação, as (contra­) propostas de um agente podem ser acompanhadas de argumentos a favor da sua aceitação. Um agente poderá, então, ter um argumento aceitável para uma sua crença, se conseguir argumentar com sucesso contra os argumentos, dos outros agentes, que o atacam. Assim, as crenças de um agente caracterizam-se pela relação entre os argumentos "internos" que sustentam suas crenças, e os argumentos "externos" que sustentam crenças contraditórias de outros agentes. Portanto, o raciocínio argumentativo baseia-se na "estabilidade externa" dos argumentos aceitáveis do conjunto de agentes. Neste trabalho propõe-se uma negociação baseada em argumentação em que, para chegarem a um consenso quanto ao conhecimento comum, os agentes constroem argumentos que sustentam as suas crenças ou que se opõem aos argumentos dos agentes que as contradizem. Além disso, esta proposta lida com conhecimento incompleto (i.e., argumentos parciais) pela definição de um processo de cooperação que permite completar tal conhecimento. Assim, a negociação entre agentes é um processo argumentativo-cooperativo, em que se podem alternar os argumentos contra e a favor das crenças de um agente. Para a formação das suas crenças, a cada agente Ag está associado um conjunto Cooperate de agentes com quem coopera e um outro Argue de agentes contra quem argumenta. A negociação proposta permite a modelação de bases de conhecimento hierárquicas, representando, por exemplo, a estrutura de uma organização ou uma taxonomia nalgum domínio, e de ambientes multi-agente em que cada agente representa o conhecimento referente a um determinado período de tempo. Um agente também pode ser inquirido sobre a verdade de uma crença, dependendo a resposta do agente em questão e de quais os agentes que com ele cooperam e que a ele se opõem. Essa resposta será, no entanto, sempre consistente/ paraconsistente com as bases de conhecimento dos agentes envolvidos. Esta dissertação propõe semânticas (declarativa e operacional) da argumentação numa base de conhecimento de um agente. Partindo destas, propõe, também, semântica declarativa da negociação baseada em argumentação num ambiente multi-agente. ⓿⓿⓿ ABSTRACT: The main objective of this dissertation is to define an argumentation-based negotiation framework for distributed knowledge bases. Knowledge bases are modelling over a multi-agent setting such that each agent possibly has an independent or overlapping knowledge base. The minimum requirement for a multi-agent setting negotiation is that agents should be able to make proposals which can then either be accepted or rejected. A higher level of sophistication occurs when recipients do not just have the choice of accepting or rejecting proposals, but have the option of making counter offers to alter aspects of the proposal which are unsatisfactory. An even more elaborate kind of negotiation is argumentation-based. The argumentation metaphor seems to be adequate for modelling situations where different agents argue in order to determine the meaning of common beliefs. ln an argumentation-based negotiation, the agents are able to send justifications or arguments along with (counter) proposals indicating why they should be accepted. An argument for an agent's belief is acceptable if the agent can argue successfully against attacking arguments from other agents. Thus, agent's beliefs are characterized by the relation between its "internal" arguments supporting its beliefs and the "external" arguments supporting the contradictory beliefs of other agents. So, in a certain sense, argumentative reasoning is based on the "external stability" of acceptable arguments in the multi-agent setting. This dissertation proposes that agents evaluate arguments to obtain a consensus about a common knowledge by both proposing arguments or trying to build opposing arguments against them. Moreover, this proposal deals with incomplete knowledge (i.e. partial arguments) and so a cooperation process grants arguments to achieve knowledge completeness. Therefore, a negotiation of an agent's belief is seen as an argumentation-based process with cooperation; both cooperation and argumentation are seen as interlaced processes. Furthermore, each agent Ag has both set Argue of argumentative agents and set Cooperate of cooperative agents; every Ag must reach a consensus on its arguments with agents in Argue, and Ag may ask for arguments from agents in Cooperate to complete its partial arguments. The argumentation-based negotiation proposal allows the modelling a hierarchy of knowledge bases representing, for instance, a business's organization or a taxonomy of some subject, and also an MAS where each agent represents "acquired knowledge" in a different period of time. Furthermore, any agent in an MAS can be queried regarding the truth value of some belief. It depends on from which agent such a belief is inferred, and also what the specification in both Argue and Cooperate is, given the overall agents in the MAS. However, such an answer will always be consistent/paraconsistent with the agents' knowledge base involved. This dissertation proposes a (declarative and operational) argumentation semantics for an agent's knowledge base. Furthermore, it proposes a declarative argumentation-based negotiation semantics for a multi-agent setting, which uses most of the definitions from the former semantics

On the equivalence between logic programming semantics and argumentation semantics

This work has been supported by the National Research Fund, Luxembourg (LAAMI project), by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant Ref. EP/J012084/1 (SAsSy project), by CNPq (Universal 2012 – Proc. 473110/2012-1), and by CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPreprin

Semantics of logic programs with explicit negation

After a historical introduction, the bulk of the thesis concerns the study of a declarative semantics for logic programs. The main original contributions are: ² WFSX (Well–Founded Semantics with eXplicit negation), a new semantics for logic programs with explicit negation (i.e. extended logic programs), which compares favourably in its properties with other extant semantics. ² A generic characterization schema that facilitates comparisons among a diversity of semantics of extended logic programs, including WFSX. ² An autoepistemic and a default logic corresponding to WFSX, which solve existing problems of the classical approaches to autoepistemic and default logics, and clarify the meaning of explicit negation in logic programs. ² A framework for defining a spectrum of semantics of extended logic programs based on the abduction of negative hypotheses. This framework allows for the characterization of different levels of scepticism/credulity, consensuality, and argumentation. One of the semantics of abduction coincides with WFSX. ² O–semantics, a semantics that uniquely adds more CWA hypotheses to WFSX. The techniques used for doing so are applicable as well to the well–founded semantics of normal logic programs. ² By introducing explicit negation into logic programs contradiction may appear. I present two approaches for dealing with contradiction, and show their equivalence. One of the approaches consists in avoiding contradiction, and is based on restrictions in the adoption of abductive hypotheses. The other approach consists in removing contradiction, and is based in a transformation of contradictory programs into noncontradictory ones, guided by the reasons for contradiction

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general

Defeasible Logic Programming: An Argumentative Approach

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, ie, the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.Comment: 43 pages, to appear in the journal "Theory and Practice of Logic Programming

Generalizations of dung frameworks and their role in formal argumentation

This article provides a short survey of some of the most popular abstract argumentation frameworks available today. The authors present the general idea of abstract argumentation, highlighting the role of abstract frameworks in the argumentation process, and review the original Dung frameworks and their semantics. A discussion of generalizations of these frameworks follows, focusing on structures taking preferences and values into account and approaches in which not only attack but also support relations can be modeled. Finally, the authors review the concept of abstract dialectical frameworks, one of the most general systems for abstract argumentation providing a flexible, principled representation of arbitrary argument relations