Verification in incomplete argumentation frameworks

This paper introduces Input/Output Argumentation Frameworks, a novel approach to characterize the behavior of an argumentation framework as a sort of black box exposing a well-defined external interface. As a starting point, we define the novel notion of semantics decomposability and analyze complete, stable, grounded and preferred semantics in this respect. Then we show as a main result that, under grounded, complete, stable and credulous preferred semantics, Input/Output Argumentation Frameworks with the same behavior can be interchanged without affecting the result of semantics evaluation of other arguments interacting with them.

Claim-augmented argumentation frameworks (CAFs) constitute a generic formalism for conflict resolution of conclusion-oriented problems in argumentation. CAFs extend Dung argumentation frameworks (AFs) by assigning a claim to each argument. So far, semantics for CAFs are defined with respect to the underlying AF by interpreting the extensions of the respective AF semantics in terms of the claims of the accepted arguments; we refer to them as inherited semantics of CAFs.<br>A central concept of many argumentation semantics is maximization, which can be done with respect to arguments as in preferred semantics, or with respect to the range as in semi-stable semantics. However, common instantiations of argumentation frameworks require maximality on the claim-level and inherited semantics often fail to provide maximal claim-sets even if the underlying AF semantics yields maximal argument sets. To address this issue, we investigate a different approach and introduce claim-level semantics (cl-semantics) for CAFs where maximization is performed on the claim-level. We compare these two approaches for five prominent semantics (preferred, naive, stable, semi-stable, and stage) and relate in total eleven CAF semantics to each other. Moreover, we show that for a certain subclass of CAFs, namely well-formed CAFs, the different versions of preferred and stable semantics coincide, which is not the case for the remaining semantics. We furthermore investigate a recently established translation between well-formed CAFs and SETAFs and show that, in contrast to the inherited naive, semi-stable and stage semantics, the cl-semantics correspond to the respective SETAF semantics. Finally, we investigate the expressiveness of the considered semantics in terms of their signatures.

argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.

Control argumentation frameworks (CAFs) [4] extend the standard model of argumentation framework (AF) due to Dung [6] in a way that takes unquantified uncertainty regarding arguments and attacks into account. Complementing recent work by Skiba et al. [21] for incomplete argumentation frameworks, we study the (nonempty) existence problem for CAFs and fully analyze its computational complexity for the most common semantics.

We introduce Incomplete Bipolar Argumentation Frameworks (iBAFs), the extension of Dung’s Abstract Argumentation Frameworks (AAFs) allowing the simultaneous presence of supports (borrowed from BAFs – Bipolar AAFs) and of uncertain elements of the argumentation graph (borrowed from iAAFs – incomplete AAFs). We investigate the computational complexity of verification problem (under the possible perspective) and the acceptance problem, by studying its sensitivity to the semantics of supports and the semantics of extensions. On the one hand, we show that adding supports on top of incompleteness does not affect the complexity of the acceptance. On the other hand, surprisingly, we show that the joint use of bipolarity and incompleteness has a deep impact on the complexity of the verification: for the semantics under which the verification over AAFs is polynomial-time solvable, although moving from AAFs to BAFs or to iAAFs does not change the complexity, the complexity of the verification over iBAFs may increase up to NP-complete.

argumentation, as originally defined by Dung, is a model that allows the description of certain information about arguments and relationships between them: in an abstract argumentation framework (AF), the agent knows for sure whether a given argument or attack exists. It means that the absence of an attack between two arguments can be interpreted as “we know that the first argument does not attack the second one”. But the question of uncertainty in abstract argumentation has received much attention in the last years. In this paper, we survey approaches that allow to express information like “There may (or may not) be an attack between these arguments”. We describe the main models that incorporate qualitative uncertainty (or ignorance) in abstract argumentation, as well as some applications of these models. We also highlight some open questions that deserve some attention in the future.

We propose natural generalizations of the credulous and skeptical acceptance problems in abstract argumentation for incomplete argumentation frameworks [3]. This continues earlier work on a similar generalization of the verification problem. We provide a full analysis of the computational complexity of the generalized problems for all original semantics, showing that, in almost all cases, acceptance problems for incomplete argumentation frameworks are significantly harder than the respective problems for argumentation frameworks without uncertainty. All our hardness results for the classes NP, coNP, Πp2, and Σp2

In this paper, we extend the fluctuation theorems used for quantum channels to multitime processes. The fluctuation theorems for quantum channels are less restrictive. We show that the given entropy production can be equal to the result of a closed system environment. The assumption that the system evolves under a completely positive and trace preserving map is quite general, but it is more specific for cases in which the system is initially correlated with the environment. System-environment correlations arise naturally in multitime processes, with which we can give clear and physical interpretations regarding the effects of correlations. Multitime processes can provide many-body channels. The Choi state of such a many-body channel is called a process tensor. One can derive channels by executing the process tensor on a set of operations. We establish a general quantum fluctuation theorem framework for a many-body channel and its derived channels. In this framework, the effects of correlations are reflected in a Markovian property. For Markovian processes, we can extend the two-point measurement to a three-point measurement and obtain that the fluctuation theorems contain complete information about the intermediate state. For non-Markovian processes, the complete measurement of the intermediate state leads to conflicts. Therefore, we use a general measurement, which only provides partial information, for the intermediate state. The corresponding fluctuation theorems show that memory effects can reduce these fluctuations. This is consistent with the fact that system states can be recovered under non-Markovian processes.

The study of computational models for argumentation is a vibrant area of artificial intelligence and, in particular, knowledge representation and reasoning research. Arguments most often have an intrinsic structure made explicit through derivations from more basic structures. Computational models for structured argumentation enable making the internal structure of arguments explicit. Assumption-based argumentation (ABA) is a central structured formalism for argumentation in AI. In this article, we make both algorithmic and complexity-theoretic advances in the study of ABA. In terms of algorithms, we propose a new approach to reasoning in a commonly studied fragment of ABA (namely the logic programming fragment) with and without preferences. While previous approaches to reasoning over ABA frameworks apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct declarative approach to ABA reasoning by encoding ABA reasoning tasks in answer set programming. We show via an extensive empirical evaluation that our approach significantly improves on the empirical performance of current ABA reasoning systems. In terms of computational complexity, while the complexity of reasoning over ABA frameworks is well-understood, the complexity of reasoning in the ABA+ formalism integrating preferences into ABA is currently not fully established. Towards bridging this gap, our results suggest that the integration of preferential information into ABA via so-called reverse attacks results in increased problem complexity for several central argumentation semantics.

This paper presents protocols and strategies for coalition formation with incomplete information under time constraints. It focuses on strategies for coalition members to distribute revenues amongst themselves. Such strategies should preferably be stable, lead to a fair distribution, and maximize the social welfare of the agents. These properties are only partially supported by existing coalition formation mechanisms. In particular, stability and the maximization of social welfare are supported only in the case of complete information, and only at a high computational complexity. Recent studies on coalition formation with incomplete and uncertain information address revenue distribution in a naive manner. In this study we specifically refer to environments with limited computational resources and incomplete information. We propose a variety of strategies for revenue distribution, including the strategy in which the agents attempt to distribute the estimated net value of a coalition equally. A variation of the equal distribution strategy in which agents compromise and agree to a payoff lower than their estimated equal share, was specifically examined. Our experimental results show that, under time constraints, the compromise strategy is stable and increases the social welfare compared to non-compromise strategies.

We present a semantic tableaux calculus for propositional nonmonotonic modal logics, based on possible-worlds characterisations for nonmonotonic modal logics. This method is parametric with respect to both the modal logic and the preference semantics, since it handles in a uniform way the entailment problem for a wide class of nonmonotonic modal logics: McDermott and Doyle's logics and ground logics. It also achieves the computational complexity lower bounds.KeywordsModal LogicKripke ModelGround LogicDefault LogicNonmonotonic ReasoningThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A method using possible equivalence classes has been developed on information tables with missing values. The method essentially differs from the other methods in having the two features. One is to directly deal with missing values by using not actual but possible equivalence classes. The other is to consider both aspects of discernibility and indiscernibility of a missing value from another value. When information tables contain incomplete information, rough approximations are not unique. We have lower and upper bounds of the actual rough approximations. The lower and upper bounds correspond to certain and possible rough approximations, respectively. Therefore, rough approximations are twofold under incomplete information. The certain and possible rough approximations are linked with each other. The method creates the same rough approximations as the method of possible worlds. This justifies the method of possible equivalence classes. The method is free from the difficulty of computational complexity for the growth of the number of missing values. Furthermore, the method is free from the restriction that missing values may occur for only some specified attributes. Therefore, we can efficiently obtain certain and possible rough approximations between arbitrary sets of attributes having missing values.

Semantic issues connected with incomplete knowledge bases are discussed. In general, information incompleteness means the incom pleteness of given values in specified attribute domains, e. g., Codd's null value and Lipski's partial information. Another information in completeness connected with the lack of primary keys may also be considerable, and in this case the closed world assumption should not be assumed. This paper uniformly formulates these two types of in complete knowledge base and precisely defines interpretations of queries. In order to realize more intellectual questionanswering, some conditions that queries are not affected by the incompleteness are discussed.

Propositional and predicate logics of incomplete information

This paper presents the preference ratios in multiattribute evaluation (PRIME) method which supports the analysis of incomplete information in multiattribute weighting models. In PRIME, preference elicitation and synthesis is based on 1) the conversion of possibly imprecise ratio judgments into an imprecisely specified preference model, 2) the use of dominance structures and decision rules in deriving decision recommendations, and 3) the sequencing of the elicitation process into a series of elicitation tasks. This process may be continued until the most preferred alternative is identified or, alternatively, stopped with a decision recommendation if the decision maker is prepared to accept the possibility that the value of some other alternative is higher. An extensive simulation study on the computational properties of PRIME is presented. The method is illustrated with a re-analysis of an earlier case study on international oil tanker negotiations.