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.

We consider planning problems for stochastic games with objectives specified by a branching-time logic, called probabilistic computation tree logic (PCTL). This problem has been shown to be undecidable if strategies with perfect recall, i.e., history-dependent, are considered. In this paper, we show that, if restricted to co-safe properties, a subset of PCTL properties capable to specify a wide range of properties in practice including reachability ones, the problem turns to be decidable, even when the class of general strategies is considered. We also give an algorithm for solving robust stochastic planning, where a winning strategy is tolerant to some perturbations of probabilities in the model. Our result indicates that satisfiability of co-safe PCTL is decidable as well.

We present a method to calculate cost-optimal policies for co-safe linear temporal logic task specifications over a Markov decision process model of a stochastic system. Our key contribution is to address scenarios in which the task may not be achievable with probability one. We formalise a task progression metric and, using multi-objective probabilistic model checking, generate policies that are formally guaranteed to, in decreasing order of priority: maximise the probability of finishing the task; maximise progress towards completion, if this is not possible; and minimise the expected time or cost required. We illustrate and evaluate our approach in a robot task planning scenario, where the task is to visit a set of rooms that may be inaccessible during execution.

We study the computational complexity of finding maximum a posteriori configurations in Bayesian networks whose probabilities are specified by logical formulas. This approach leads to a fine grained study in which local information such as context-sensitive independence and determinism can be considered. It also allows us to characterize more precisely the jump from tractability to NP-hardness and beyond, and to consider the complexity introduced by evidence alone.

In this paper, we address the challenge of predicting optimal comfort temperatures of individual users of a smart heating system. At present, such systems use simple models of user comfort when deciding on a set point temperature. These models generally fail to adapt to an individual user’s preferences, resulting in poor estimates of a user’s preferred temperature. To address this issue, we propose a personalised thermal comfort model that uses a Bayesian network to learn and adapt to a user’s individual preferences. Through an empirical evaluation based on the ASHRAE RP-884 data set, we show that our model is consistently 17.5- 23.5% more accurate than current models, regardless of environmental conditions and the type of heating system used. Our model is not limited to a single metric but can also infer information about expected user feedback, optimal comfort temperature and thermal sensitivity at the same time, which can be used to reduce energy used for heating with minimal comfort loss.

Nowadays, multiagent planning under uncertainty scales to tens or even hundreds of agents. However, current methods either are restricted to problems with factored value functions, or provide solutions without any guarantees on quality. Methods in the former category typically build on heuristic search using upper bounds on the value function. Unfortunately, no techniques exist to compute such upper bounds for problems with non-factored value functions, which would additionally allow for meaningful benchmarking of methods of the latter category. To mitigate this problem, this paper introduces a family of influence-optimistic upper bounds for factored Dec-POMDPs without factored value functions. We demonstrate how we can achieve firm quality guarantees for problems with hundreds of agents.

Cognitive modelling can discover the latent characteristics of examinees for predicting their performance (i.e. scores) on each problem. As cognitive modelling is important for numerous applications, e.g. personalized remedy recommendation, some solutions have been designed in the literature. However, the problem of extracting information from both objective and subjective problems to get more precise and interpretable cognitive analysis is still underexplored. To this end, we propose a fuzzy cognitive diagnosis framework (FuzzyCDF) for examinees' cognitive modelling with both objective and subjective problems. Specifically, to handle the partially correct responses on subjective problems, we first fuzzify the skill proficiency of examinees. Then, we combine fuzzy set theory and educational hypotheses to model the examinees' mastery on the problems. Further, we simulate the generation of examination scores by considering both slip and guess factors. Extensive experiments on three real-world datasets prove that FuzzyCDF can predict examinee performance more effectively, and the output of FuzzyCDF is also interpretative.

Interactive dynamic influence diagrams(I-DIDs) are a well recognized decision model that explicitly considers how multiagent interaction affects individual decision making. To predict behavior of other agents, I-DIDs require models of the other agents to be known ahead of time and manually encoded. This becomes a barrier to I-DID applications in a human-agent interaction setting, such as development of intelligent non-player characters(NPCs) in real-time strategy(RTS) games, where models of other agents or human players are often inaccessible to domain experts. In this paper, we use automatic techniques for learning behavior of other agents from replay data in RTS games. We propose a learning algorithm with improvement over existing work by building a full profile of agent behavior. This is the first time that data-driven learning techniques are embedded into the I-DID decision making framework. We evaluate the performance of our approach on two test cases.

Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of ''big data,'' traditional inference algorithms for such a model are increasingly limited due to their high time complexity and poor scalability. In this paper, we propose a multi-stage maximum likelihood approach to recover the latent parameters of the stochastic block model, in time linear with respect to the number of edges. We also propose a parallel algorithm based on message passing. Our algorithm can overlap communication and computation, providing speedup without compromising accuracy as the number of processors grows. For example, to process a real-world graph with about 1.3 million nodes and 10 million edges, our algorithm requires about 6 seconds on 64 cores of a contemporary commodity Linux cluster. Experiments demonstrate that the algorithm can produce high quality results on both benchmark and real-world graphs. An example of finding more meaningful communities is illustrated consequently in comparison with a popular modularity maximization algorithm.

Weighted model counting (WMC) on a propositional knowledge base is an effective and general approach to probabilistic inference in a variety of formalisms, including Bayesian and Markov Networks. However, an inherent limitation of WMC is that it only admits the inference of discrete probability distributions. In this paper, we introduce a strict generalization of WMC called weighted model integration that is based on annotating Boolean and arithmetic constraints, and combinations thereof. This methodology is shown to capture discrete, continuous and hybrid Markov networks. We then consider the task of parameter learning for a fragment of the language. An empirical evaluation demonstrates the applicability and promise of the proposal.