Jonathan Ben-Naim

Ranking-Based Semantics for Argumentation Frameworks

An argumentation system consists of a set of interacting arguments and a semantics for evaluating them. This paper proposes a new family of semantics which rank-orders arguments from the most acceptable to the weakest one(s). The new semantics enjoy two other main features: i) an attack weakens its target but does not kill it, ii) the number of attackers has a great impact on the acceptability of an argument. We start by proposing a set of rational postulates that such semantics could satisfy, then construct various semantics that enjoy them.

Cut-free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

Abstract.The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics.

Processing Information from a Set of Sources

We introduce a general framework for solving the problem of a computer collecting and combining information from various sources. Unlike previous approaches to this problem, in our framework the sources are allowed to provide information about complex formulae too. This is enabled by the use of a new tool—non-deterministic logical matrices. We also consider several alternative plausible assumptions concerning the framework which lead to various logics. We provide strongly sound and complete proof systems for all the basic logics induced in this way.

Acceptability Semantics for Weighted Argumentation Frameworks

The paper studies semantics for evaluating arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.

An Answer Set Programming Encoding of Prioritized Removed Sets Revision: Application to GIS

Geographical information systems are one of the most important application areas of belief revision. Recently, Wiirbel and colleagues [32] have applied the so-called removed sets revision (RSR) to the problem of assessment of water heights in a flooded valley. The application was partially satisfactory since only a small part of the valley has been handled. This paper goes one step further, and proposes an extension of (RSR) called Prioritized Removed Sets Revision (PRSR). We show that (PRSR) performed using answer set programming makes possible to solve a practical revision problem provided by a real application in the framework of geographical information system (GIS). We first show how PRSR can be encoded into a logic program with answer set semantics, we then present an adaptation of the smodels system devoted to efficiently compute the answer sets in order to perform PRSR. The experimental study shows that the answer set programming approach gives better results than previous implementations of RSR and in particular it allows to handle the whole valley. Lastly, some experimental studies comparing our encoding with implementations based on SAT-solvers are also provided.

Measuring the Intensity of Attacks in Argumentation Graphs with Shapley Value

In an argumentation setting, a semantics evaluates the overall acceptability of arguments. Consequently, it reveals the global loss incurred by each argument due to attacks. However, it does not say anything on the contribution of each attack to that loss. This paper introduces the novel concept of contribution measure for evaluating those contributions. It starts by defining a set of axioms that a reasonable measure would satisfy, then shows that the Shapley value is the unique measure that satisfies them. Finally, it investigates the properties of the latter under some existing semantics.

Evaluation of Arguments in Weighted Bipolar Graphs

The paper tackled the issue of arguments evaluation in weighted bipolar argumentation graphs (i.e., graphs whose arguments have basic strengths, and may be both supported and attacked). We introduce axioms that an evaluation method (or semantics) could satisfy. Such axioms are very useful for judging and comparing semantics. We then analyze existing semantics on the basis of our axioms, and finally propose a new semantics for the class of acyclic graphs.

Belief revision of GIS systems: the results of REV!GIS

This paper presents a synthesis of works performed on the practical tractability of revision on geographic information within the european REV!GIS project.It surveys di.erent representations of the revision problem as well as di.erent implementations of the adopted stategy: Removed Set Revision (RSR). A comparison of the representation formalisms is provided, a formal and an experimental comparison is conducted on the various implementations on real scale applications in the context of GIS.

Preferential and Preferential-discriminative Consequence Relations

The theory of preferential consequence relations has been investigated extensively in the classical context, where copies of classical valuations serve as the terms of the preference relation. The first purpose of the present paper is to extend the theory to preferential consequence relations in certain three/four-valued contexts, well-known as the paraconsistent logics J3 and FOUR. We give characterizations of several families of preferential consequence relations in these two contexts. Our second and main purpose is to investigate a qualified version of preferential consequence, which we call preferential-discriminative consequence. This is defined to hold between a set Γ of formulae and formula α iff Γ -- α but Γ -- ¬ α where -- is the plain relation. We provide characterizations of several families of such preferential-discriminative consequence relations for all of the classical, three, and four-valued contexts.

Argumentation-Based Paraconsistent Logics

Argumentation is a promising approach for reasoning with inconsistent information. Starting from a knowledge base encoded in a logical language, an argumentation system defines arguments and attacks between them using the consequence operator associated with the language. Finally, it uses a semantics for evaluating the arguments. The plausible conclusions to be drawn from the knowledge base are those supported by “good” arguments.