Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which alternatives have an associated vector of costs, each component corresponding to a different criterion, and are compared using a kind of lexicographic order, similar to the way alternatives are compared in a Hierarchical Constraint Logic Programming model. It is assumed that the user has some (unknown) importance ordering on criteria, and that to compare two alternatives, firstly, the combined cost of each alternative with respect to the most important criteria are compared; only if these combined costs are equal, are the next most important criteria considered. The preference inference problem then consists of determining whether a preference statement can be inferred from a set of input preferences. We show that this problem is co-NP-complete, even if one restricts the cardinality of the equal-importance sets to have at most two elements, and one only considers non-strict preferences. However, it is polynomial if it is assumed that the user's ordering of criteria is a total ordering; it is also polynomial if the sets of equally important criteria are all equivalence classes of a given fixed equivalence relation. We give an efficient polynomial algorithm for these cases, which also throws light on the structure of the inference.

The goal of query conceptualization is to map instances in a query to concepts defined in a certain ontology or knowledge base. Queries usually do not observe the syntax of a written language, nor do they contain enough signals for statistical inference. However, the available context, i.e., the verbs related to the instances, the adjectives and attributes of the instances, do provide valuable clues to understand instances. In this paper, we first mine a variety of relations among terms from a large web corpus and map them to related concepts using a probabilistic knowledge base. Then, for a given query, we conceptualize terms in the query using a random walk based iterative algorithm. Finally, we examine our method on real data and compare it to representative previous methods. The experimental results show that our method achieves higher accuracy and efficiency in query conceptualization.

Instrumental variables (IVs) are widely used to identify causal effects. For this purpose IVs have to be exogenous, i.e., causally unrelated to all variables in the model except the explanatory variable X . It can be hard to find such variables. A generalized IV method has been proposed that only requires exogeneity conditional on a set of covariates. This leads to a wider choice of potential IVs, but is rarely used yet. Here we address two issues with conditional IVs. First, they are conceptually rather distant to standard IVs; even variables that are independent of X could qualify as conditional IVs. We propose a new concept called ancestral IV , which interpolates between the two existing notions. Second, so far only exponential-time algorithms are known to find conditional IVs in a given causal diagram. Indeed, we prove that this problem is NP-hard. Nevertheless, we show that whenever a conditional IV exists, so does an ancestral IV, and ancestral IVs can be found in polynomial time. Together this implies a complete and constructive solution to causal effect identification using IVs in linear causal models.

For instance, does it form a "nice" class, which can be characterized A formal framework is given for the postulate characterizability by postulates? of a class of belief revision operators, Proving non-characterizability presupposes a formal definition obtained from a class of partial preorders using of a postulate. However, as noted in the survey [Fermé minimization. It is shown that for classes of posets and Hansson, 2011] characterizability is equivalent to a special kind of "theories of belief change developed in the AGM definability in monadic second-order logic, which tradition are not logics in a strict sense, but rather turns out to be incomparable to first-order definability.

RCC8 is a constraint language that serves for qualitative spatial representation and reasoning by encoding the topological relations between spatial entities. We focus on efficiently characterizing non-redundant constraints in large real world RCC8 networks and obtaining their prime networks. For a RCC8 network N a constraint is redundant, if removing that constraint from N does not change the solution set of N. A prime network of N is a network which contains no redundant constraints, but has the same solution set as N. We make use of a particular partial consistency, namely, G-path consistency, and obtain new complexity results for various cases of RCC8 networks, while we also show that given a maximal distributive subclass for RCC8 and a network N defined on that subclass, the prunning capacity of G-path consistency and path consistency is identical on the common edges of G and the complete graph of N, when G is a triangulation of the constraint graph of N. Finally, we devise an algorithm based on G-path consistency to compute the unique prime network of a RCC8 network, and show that it significantly progresses the state-of-the-art for practical reasoning with real RCC8 networks scaling up to millions of nodes.

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.

Fundamental to reasoning about actions and beliefs is the projection problem: to decide what is believed after a sequence of actions is performed. Progression is one widely applied technique to solve this problem. In this paper we propose a novel framework for computing progression in the epistemic situation calculus. In particular, we model an agent's preferential belief structure using conditional statements and provide a technique for updating these conditional statements as actions are performed and sensing information is received. Moreover, we show, by using the concepts of natural revision and only-believing, that the progression of a conditional knowledge base can be represented by only-believing the revised set of conditional statements. These results lay the foundations for feasible belief progression due to the unique-model property of only-believing.

We introduce a framework for qualitative reasoning about directions in high-dimensional spaces, called EER, where our main motivation is to develop a form of commonsense reasoning about semantic spaces. The proposed framework is, however, more general; we show how qualitative spatial reasoning about points with several existing calculi can be reduced to the realisability problem for EER (or REER for short), including LR and calculi for reasoning about betweenness, collinearity and parallelism. Finally, we propose an efficient but incomplete inference method, and show its effectiveness for reasoning with EER as well as reasoning with some of the aforementioned calculi.

Existential rules (also known as Datalog+/- or tuple-generating dependencies) have been intensively studied in recent years as a prominent formalism in knowledge representation and database systems. We consider them here as a querying formalism, extending classical Datalog, the language of deductive databases. It is well known that the classes of databases recognized by (Boolean) existential rule queries are closed under homomorphisms. Also, due to the existence of a semi-decision procedure (the chase), these database classes are recursively enumerable. We show that, conversely, every homomorphism-closed recursively enumerable query can be expressed as an existential rule query, thus arriving at a precise characterization of existential rules by model-theoretic and computational properties. Although the result is very intuitive, the proof turns out to be non-trivial. This result can be seen as a very expressive counterpart of the prominent Lyndon-Los-Tarski-Theorem characterizing the homomorphism-closed fragment of first-order logic. Notably, our result does not presume the existence of any additional built-in structure on the queried data, such as a linear order on the domain, which is a typical requirement for other characterizations in the spirit of descriptive complexity.

Formal Concept Analysis (FCA) is a prominent field of applied mathematics using object-attribute relationships to define formal concepts — groups of objects with common attributes — which can be ordered into conceptual hierarchies, so-called concept lattices. We consider the problem of satisfiability of membership constraints, i.e., to determine if a formal concept exists whose object and attribute set include certain elements and exclude others. We analyze the computational complexity of this problem in general and for restricted forms of membership constraints. We perform the same analysis for generalizations of FCA to incidence structures of arity three (objects, attributes and conditions) and higher. We present a generic answer set programming (ASP) encoding of the membership constraint satisfaction problem, which allows for deploying available highly optimized ASP tools for its solution. Finally, we discuss the importance of membership constraints in the context of navigational approaches to data analysis.