This paper relates two extensively studied formalisms: abstract dialectical frameworks and logic programs with generalized atoms or similar constructs. While the syntactic similarity is easy to see, also a strong relation between various stable model semantics proposed for these formalisms is shown by means of a unifying framework in which these semantics are restated in terms of program reducts and an immediate consequence operator, where program reducts have only minimal differences. This approach has advantages for both formalisms, as for example implemented systems for one formalism are usable for the other, and properties such as computational complexity do not have to be rediscovered. As a first, concrete result of this kind, one stable model semantics based on program reducts and subset-minimality that reached a reasonable consensus for logic programs with generalized atoms provides a novel, alternative semantics for abstract dialectical frameworks.

The computation of minimal conflict sets is a central task when the goal is to find relaxations or explanations for overconstrained problem formulations and in particular in the context of Model-Based Diagnosis (MBD) approaches. In this paper we propose MergeXPlain, a non-intrusive conflict detection algorithm which implements a divide-and-conquer strategy to decompose a problem into a set of smaller independent subproblems. Our technique allows us to efficiently determine multiple minimal conflicts during one single problem decomposition run, which is particularly helpful in MBD problem settings. An empirical evaluation on various benchmark problems shows that our method can lead to a significant reduction of the required diagnosis times.

The square of opposition is a structure involving two involutive negations and relating quantified statements, invented in Aristotle time. Rediscovered in the second half of the XXth century, and advocated as being of interest for understanding conceptual structures and solving problems in paraconsistent logics, the square of opposition has been recently completed into a cube, which corresponds to the introduction of a third negation. Such a cube can be encountered in very different knowledge representation formalisms, such as modal logic, possibility theory in its all-or-nothing version, formal concept analysis, rough set theory and abstract argumentation. After restating these results in a unified perspective, the paper proposes a graded extension of the cube and shows that several qualitative, as well as quantitative formalisms, such as Sugeno integrals used in multiple criteria aggregation and qualitative decision theory, or yet belief functions and Choquet integrals, are amenable to transformations that form graded cubes of opposition. This discovery leads to a new perspective on many knowledge representation formalisms, laying bare their underlying common features. The cube of opposition exhibits fruitful parallelisms between different formalisms, which leads to highlight some missing components present in one formalism and currently absent from another.

The ability to perform reasoning on inconsistent data is a central problem both for AI and database research. One approach to deal with this situation is consistent query answering, where queries are answered over all possible repairs of the database. In general, the repair may be very distant from the original database. In this work we present a new approach where this distance is bounded and analyze its computational complexity. Our results show that in many (but not all) cases the complexity drops.

We study equilibrium dynamics in candidacy games, in which candidates may strategically decide to enter the election or withdraw their candidacy, following their own preferences over possible outcomes. Focusing on games under Plurality, we extend the standard model to allow for situations where voters may refuse to return their votes to those candidates who had previously left the election, should they decide to run again. We show that if at the time when a candidate withdraws his candidacy, with some positive probability each voter takes this candidate out of his future consideration, the process converges with probability 1. This is in sharp contrast with the original model where the very existence of a Nash equilibrium is not guaranteed. We then consider the two extreme cases of this setting, where voters may block a withdrawn candidate with probabilities 0 or 1. In these scenarios, we study the complexity of reaching equilibria from a given initial point, converging to an equilibrium with a predermined winner or to an equilibrium with a given set of running candidates. Except for one easy case, we show that these problems are NP-complete, even when the initial point is fixed to a natural---truthful---state where all potential candidates stand for election.

Hedonic games provide a natural model of coalition formation among self-interested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on expressivity of hedonic games that are sufficient for the problem of checking whether a given game admits a stable outcome to be computationally hard. Somewhat surprisingly, these conditions are very mild and intuitive. Our results apply to a wide range of stability concepts (core stability, individual stability, Nash stability, etc.) and to many known formalisms for hedonic games (additively separable games, games with W-preferences, fractional hedonic games, etc.), and unify and extend known results for these formalisms. They also have broader applicability: for several classes of hedonic games whose computational complexity has not been explored in prior work, we show that our framework immediately implies a number of hardness results for them.

Core-guided MAXSAT algorithms dominate other methods in solving industrial MAXSAT problems. In this work, we propose a new efficient algorithm that is guided by correction sets and cores. At every iteration, the algorithm obtains a correction set or a core, which is then used to rewrite the formula using incremental and succinct transformations. We theoretically show that correction sets and cores have complementary strengths and empirically demonstrate that their combination leads to an efficient MAXSAT solver that outperforms state-of-the-art WPMS solvers on the 2014 Evaluation on industrial instances.

In this paper, we develop a novel graph kernel by aligning the Jensen-Shannon (JS) representations of vertices. We commence by describing how to compute the JS representation of a vertex by measuring the JS divergence (JSD) between the corresponding $-layer depth-based (DB) representations developed. By aligning JS representations of vertices, we identify the correspondence between the vertices of two graphs and this allows us to construct a matching-based graph kernel. Unlike existing R-convolution kernels that roughly record the isomorphism information between any pair of substructures under a type of graph decomposition, the new kernel can be seen as an aligned subgraph kernel that incorporates explicit local correspondences of substructures i.e., the local information graphs) into the process of kernelization through the JS representation alignment. The new kernel thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments demonstrate that our kernel can easily outperform state-of-the-art graph kernels in terms of the classification accuracies.

The AGM theory of belief revision is based on propositional belief sets. In this paper we develop a logic for revision of temporal belief bases, containing expressions about temporal propositions (tomorrow it will rain), possibility (it may rain tomorrow), actions (the robot enters the room) and pre- and post-conditions of these actions. We prove the Katsuno-Mendelzon and the Darwiche-Pearl representation theorems by restricting the logic to formulas representing beliefs up to certain time. We illustrate our belief change model through several examples.

We propose new mechanisms that can be used by a demand response aggregator to flexibly shift the charging of electric vehicles (EVs) to times where cheap but intermittent renewable energy is in high supply. Here, it is important to consider the constraints and preferences of EV owners, while eliminating the scope for strategic behaviour. To achieve this, we propose, for the first time, a generic class of incentive mechanisms for settings with both varying marginal electricity costs and multidimensional preferences. We show these are dominant strategy incentive compatible, i.e., EV owners are incentivised to report their constraints and preferences truthfully. We also detail a specific instance of this class, show that it achieves ≈98% of the optimal in realistic scenarios and demonstrate how it can be adapted to trade off efficiency with profit.