ABSTRACT. Possibilistic logic (PL) is more than thirty years old. The paper proposes a survey of its main developments and applications in artificial intelligence, together with a short presentation of works in progress. PL amounts to a classical logic handling of certainty-qualified statements. Certainty is estimated in the setting of possibility theory as a lower bound of a necessity set-function. An elementary possibilistic formula is a pair made of a classical logic formula, and a certainty level belonging to a bounded scale. Basic PL handles only conjunctions of such formulas, and PL bases can be viewed as classical logic bases layered in terms of certainty. Semantics is in terms of epistemic states represented by fuzzy sets of interpretations. A PL base is associated with an inconsistency level above which formulas are safe from inconsistency. Applications include reasoning with default rules, belief revision, Bayesian possibilistic networks, information fusion, and preference modeling (in this latter case, certainty is turned into priority). Different extensions of basic PL are briefly reviewed, where levels take values in lattices, are replaced by vectors of levels, or are handled in a purely symbolic manner (without being instantiated). This latter extension may be of interest for explanation purposes. A paraconsistent treatment of inconsistency is also discussed. Still another extension allows for associating possibilistic formulas with sets of agents or sources that support them. In generalized possibilistic logic (GPL), negation and disjunction can be applied as well as conjunction, to possibilistic formulas. It may be viewed as a fragment of modal logic (such as KD45) where modalities cannot be nested. GPL can be still extended to a logic involving both objective and non-nested multimodal formulas. Applications of GPL to the modeling of ignorance, to the representation of answer set programs, to reasoning about other agents’ beliefs, and to a logic of argumentation are outlined. Generally speaking, the interest and the strength of possibilistic relies on a sound alliance between classical logic and possibility theory which offers a rich representation setting allowing an accurate representation of partial ignorance. The presentation focuses more on ideas than on technicalities and refers to references for details. The talk is presented by the second author.

ABSTRACT. A fast-growing research direction in the study of formal argumentation is the development of practical systems for central reasoning problems underlying argumentation. In particular, numerous systems for abstract argumentation frameworks (AF solvers) are available today, covering several argumentation semantics and reasoning tasks. Instead of proposing another algorithmic approach for AF solving, we introduce in this paper distinct AF preprocessing techniques as a solver-independent approach to obtaining performance improvements of AF solvers. We establish a formal framework of replacement patterns to perform local simplifications that are faithful with respect to standard semantics for AFs. Moreover, we provide a collection of concrete replacement patterns. Towards practical applicability, we employ the patterns in a preliminary empirical evaluation of their influence on AF solver performance.

ABSTRACT. The aim of the paper is to combine two of the most important areas of knowledge representation, namely belief revision and argumentation. More precisely, we present a first study of AGM-style contraction for abstract argumentation frameworks (AFs). Contraction deals with removing former beliefs from a given knowledge base. Our presented approach is based on a reformulation of the original AGM postulates. In contrast to the AGM setup where propositional logic is used we build upon the recently developed Dung-logics. These logics have been introduced to tackle the somehow inverse problem, namely adding new beliefs. Importantly, they satisfy the following characterization property, namely ordinary equivalence in Dung logics coincides with strong equivalence for the respective argumentation semantics. Although using the same setup we proved a negative result regarding the unrestricted existence of contraction operators. This means, an analog to the Harper Identity, which allows to construct a contraction operator from a given revision operator, is not available. However, dropping the somewhat controversial recovery postulate leads to the existence of reasonable operators.

ABSTRACT. After Dung's founding work in Abstract Argumentation Frameworks there has been a growing interest in extending the Dung's semantics in order to describe more complex or real life situations. Several of these approaches take the direction of weighted or probabilistic extensions. One of the most prominent probabilistic approaches is that of constellation Probabilistic Abstract Argumentation Frameworks.

In this paper, we first introduce the probabilistic attack normal form for the constellation semantics; we then prove that the probabilistic attack normal form is sufficient to represent any Probabilistic Abstract Argumentation Framework of the constellation semantics; and finally, we illustrate its connection with Probabilistic Logic Programming.

ABSTRACT. We revise classical properties of Abstract Argumentation Frameworks in presence of weights on attacks. We focus on the notion of well-foundedness originally provided by P. M. Dung in his pioneering work. We generalise it by considering sequences of Set Minimal Attack sets, instead of a plain sequence of arguments: such sets include all the arguments attacking a previous set in the sequence. By using a parametric framework based on the algebraic structure, we are able to study different proposals of weighted defence in the literature, and consequently relate their well-foundedness. We generalise such a property to any weighted defence, but also to original Dung’s defence. Finally, we provide conditions for the uniqueness of the preferred and existence of the stable extensions.

ABSTRACT. Minimal inconsistent subsets of knowledge bases in monotonic logics play an important role when investigating the reasons for conflicts and trying to handle them. In the context of non-monotonic reasoning this notion is not as meaningful due to the possibility of resolving conflicts by adding information. In this paper we investigate inconsistency in non-monotonic logics while taking this issue into account. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics even if we allow adding novel information to a given knowledge base. We illustrate the versatility of the main theorems by covering more sophisticated situations and demonstrate how to utilize our results to analyze inconsistency in abstract argumentation.

ABSTRACT. Abstract dialectical frameworks (ADFs) are generalizations of Dung's argumentation frameworks which allow arbitrary relationships among arguments to be expressed. In particular, arguments can not only attack each other, they also may provide support for other arguments and interact in various complex ways. The ADF approach has recently been extended in two different ways. On the one hand, GRAPPA is a framework that applies the key notions underlying ADFs - in particular their operator-based semantics - directly to arbitrary labelled graphs. This allows users to represent argumentation scenarios in their favourite graphical representations without giving up the firm ground of well-defined semantics. On the other hand, ADFs have been further generalized to the multi-valued case to enable fine-grained acceptance values. In this paper we unify these approaches and develop a multi-valued version of GRAPPA combining the advantages of both extensions.

ABSTRACT. Automated reasoning techniques for multi-agent scenarios need to address the possibility that procedures for collective decision making may fall prey to manipulation by self-interested agents. In this paper we study manipulation in the context of belief merging, a framework for aggregating agents' positions, or beliefs, with respect to a set of issues represented by propositional atoms. Within this framework agents submit their positions as propositional formulas that are to be aggregated into a single formula. To reach a final decision, we employ well-established acceptance notions and extract the skeptical and credulous consequences (i.e., atoms true in all and, respectively, at least one model) of the resulting formula. We find that, even in restricted cases, most aggregation procedures are vulnerable to manipulation by an agent acting strategically, i.e., one that is able to submit a formula not representing its true position. Our results apply when the goal of such an agent is either that of (i) affecting an atom's skeptical or credulous acceptance status, or (ii) improving its satisfaction with the result. With respect to latter task, we extend existing work on manipulation with new satisfaction indices, based on skeptical and credulous reasoning. We also study the extent to which an agent can influence the outcome of the aggregation, and show that manipulation can often be achieved by submitting a complete formula (i.e., a formula having exactly one model), yet, the complexity of finding such a formula resides, in the general case, on the second level of the polynomial hierarchy.

ABSTRACT. In abstract argumentation, multiple argumentation semantics have been proposed that allow to select sets of jointly acceptable arguments from a given argumentation framework, i.e. based only on the attack relation between arguments. The existence of multiple argumentation semantics raises the question which of these semantics predicts best how humans evaluate arguments. Previous empirical cognitive studies that have tested how humans evaluate sets of arguments depending on the attack relation between them have been limited to a small set of very simple argumentation frameworks, so that some semantics studied in the literature could not be meaningfully distinguished by these studies. In this paper we report on an empirical cognitive study that overcomes these limitations by taking into consideration twelve argumentation frameworks of three to eight arguments each. These argumentation frameworks were mostly more complex than the argumentation frameworks considered in previous studies. All twelve argumentation framework were systematically instantiated with natural language arguments based on a certain fictional scenario, and participants were shown both the natural language arguments and a graphical depiction of the attack relation between them. Our data shows that grounded and CF2 semantics were the best predictors of human argument evaluation. A detailed analysis revealed that part of the participants chose a cognitively simpler strategy that is predicted very well by grounded semantics, while another part of the participants chose a cognitively more demanding strategy that is mostly predicted well by CF2 semantics.

ABSTRACT. Ontology-mediated query answering is an important paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. We propose a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic ELH-bottom, which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity.

ABSTRACT. A distinguishing feature of Answer Set Programming is that all atoms belonging to a stable model must be founded. That is, an atom must not only be true but provably true. This can be made precise by means of the constructive logic of Here-and-There, whose equilibrium models correspond to stable models. One way looking at foundedness is to regard Boolean truth values as ordered by letting true be greater than false. Then, each Boolean variable takes the smallest truth value that can be proven for it. This idea was generalized by Aziz et al to ordered domains and applied to constraint satisfaction problems. As before, the idea is that a, say integer, variable gets only assigned to the smallest integer that can be justied. In this paper, we present a logical reconstruction of Aziz' idea in the setting of the logic of Here-and-There. More precisely, we start by defining the logic of Here-and-There with lower bound founded variables along with its equilibrium models and elaborate upon their formal properties. Finally, we compare our approach with related ones and sketch future work.

ABSTRACT. In Digital Forensic and Digital Investigations, the "Evidence Analysis" phase has the aim to extract elements of proof from digital evidence of any kind, to be presented and discussed in court. The aim of the European Action DigForASP: "DIGital FORensics, evidence Analysis via intelligent Systems and Practices" is to explore the applicability of artificial intelligence (AI) along with computational logic tools -- and in particular the Answer Set Programming (ASP) approach -- to the automation of Evidence Analysis. In this talk we will illustrate the Action structure and objectives and, by means of case studies, the preliminary results that we have reached.