Reasoning with Inconsistencies in Propositional Peer-to-Peer Inference Systems

International audiencen a peer-to-peer inference system, there is no centralized control or hierarchical organization: each peer is equivalent in functionality and cooperates with other peers in order to solve a collective reasoning task. Since peer theories model possibly different viewpoints, even if each local theory is consistent, the global theory may be inconsistent. We exhibit a distributed algorithm detecting inconsistencies in a fully decentralized setting. We provide a fully distributed reasoning algorithm, which computes only well-founded consequences of a formula, i.e., with a consistent set of support

Postulates for logic-based argumentation systems

International audienceLogic-based argumentation systems are developed for reasoning with inconsistent information. Starting from a knowledge base encoded in a logical language, they define arguments and attacks between them using the consequence operator associated with the language. Finally, a semantics is used for evaluating the arguments. In this paper, we focus on systems that are based on deductive logics and that use Dung's semantics. We investigate rationality postulates that such systems should satisfy. We define five intuitive postulates: consistency and closure under the consequence operator of the underlying logic of the set of conclusions of arguments of each extension, closure under sub-arguments and exhaustiveness of the extensions, and a free precedence postulate ensuring that the free formulas of the knowledge base (i.e., the ones that are not involved in inconsistency) are conclusions of arguments in every extension. We study the links between the postulates and explore conditions under which they are guaranteed or violated

Rich preference-based argumentation frameworks

International audienceAn argumentation framework is seen as a directed graph whose nodes are arguments and arcs are attacks between the arguments. Acceptable sets of arguments, called extensions, are computed using a semantics. Existing semantics are solely based on the attacks and do not take into account other important criteria like the intrinsic strengths of arguments. The contribution of this paper is three fold. First, we study how preferences issued from differences in strengths of arguments can help in argumentation frameworks. We show that they play two distinct and complementary roles: (i) to repair the attack relation between arguments, (ii) to refine the evaluation of arguments. Despite the importance of both roles, only the first one is tackled in existing literature. In a second part of this paper, we start by showing that existing models that repair the attack relation with preferences do not perform well in certain situations and may return counter-intuitive results. We then propose a new abstract and general framework which treats properly both roles of preferences. The third part of this work is devoted to defining a bridge between the argumentation-based and the coherence-based approaches for handling inconsistency in knowledge bases, in particular when priorities between formulae are available. We focus on two well-known models, namely the preferred sub-theories introduced by Brewka and the demo-preferred sets defined by Cayrol, Royer and Saurel. For each of these models, we provide an instantiation of our abstract framework which is in full correspondence with it

A postulate-driven study of logical argumentation

Logical argumentation is a well-known approach to modeling non-monotonic reasoning with conflicting information. In this paper we provide a comprehensive postulate-based study of properties of logical argumentation frameworks and a full characterization of their semantics and inference relations. In this way we identify well-behaved formal argumentative models of drawing logically justified inferences from a given set of possibly conflicting defeasible, as well as strict assumptions. Given some desiderata in terms of rationality postulates, we consider the conditions that an argumentation framework should fulfill for the desiderata to hold. One purpose of this approach is to assist designers to “plug-in” pre-defined formalisms according to actual needs. To this end, we present a classification of argumentation frameworks relative to the types of attacks they implement. In turn, for each class we determine which desiderata are satisfied. Our study is highly abstract, supposing only a minimal set of requirements on the considered underlying deductive systems, and in this way covering a broad range of formalisms, including classical, intuitionistic and modal logics

A Purely Defeasible Argumentation Framework

Argumentation theory is concerned with the way that intelligent agents discuss whether some statement holds. It is a claim-based theory that is widely used in many areas, such as law, linguistics and computer science. In the past few years, formal argumentation frameworks have been heavily studied and applications have been proposed in fields such as natural language processing, the semantic web and multi-agent systems. Studying argumentation provides results which help in developing tools and applications in these areas. Argumentation is interesting as a logic-based approach to deal with inconsistent information. Arguments are constructed using a process like logical inference, with inconsistencies giving rise to conflicts between arguments. These conflicts can then be handled by well-founded means, giving a consistent set of well-justified arguments and conclusions. Dung\u27s seminal work tells us how to handle the conflicts between arguments. However, it says nothing about the structure of arguments, or how to construct arguments and attack relationships from a knowledge base. ASPIC+ is one of the most widely used systems for structured arguments. However, there are some limitations on ASPIC+ if it is to satisfy widely accepted standards of rationality. Since most of these limitations are due to the use of strict rules, it is worth considering using a purely defeasible subset of ASPIC+. The main contribution of this dissertation is the purely defeasible argumentation framework ASPIC+D. There are three research questions related to this topic which are investigated here: (1) Do we lose anything in removing the strict elements? (2) Do purely defeasible version of theories generate the same results as the original theories? (3) What do we gain by removing the strict elements? I show that using ASPIC+D, it is possible, in a well-defined sense, to capture the same information as using ASPIC+ with strict rules. In particular, I prove that under some reasonable assumptions, it is possible to take a well-defined theory in ASPIC+, that is one with a consistent set of conclusions, and translate it into ASPIC+D such that, under the grounded semantics, we obtain the same set of justified conclusions. I also show that, under some additional assumptions, the same is true under any complete-based semantics. Furthermore, I formally characterize the situations in which translating an ASPIC+ theory that is ill-defined into ASPIC+D will lead to the same sets of justified conclusions. In doing this I deal both with ASPIC+ theories that are not closed under transposition and theories that are axiom inconsistent. At last, I analyze the two systems in the context of the non-monotonic axioms. I show that ASPIC+ and ASPIC+D satisfy exactly same axioms under what I call the “argument construction” interpretation and the “justified conclusions” interpretation under the grounded semantics. Furthermore, because of the lack of strict elements, ASPIC+ satisfies more of the non-monotonic axioms than ASPIC+ in the ``justified conclusions\u27\u27 interpretation under the preferred semantic. This means that ASPIC+ and ASPIC+D may not have the same justified conclusions under the preferred semantics

Complexity classifications for nonmonotonic reasoning and enumeration

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