Many applications of causal inference, such as finding the relationship between stock prices and news reports, involve both discrete and continuous variables observed over time. Inference with these complex sets of temporal data, though, has remained difficult and required a number of simplifications. We show that recent approaches for inferring temporal relationships (represented as logical formulas) can be adapted for inference with continuous valued effects. Building on advances in logic, PCTLc (an extension of PCTL with numerical constraints) is introduced here to allow representation and inference of relationships with a mixture of discrete and continuous components. Then, finding significant relationships in the continuous case can be done using the conditional expectation of an effect, rather than its conditional probability. We evaluate this approach on both synthetically generated and actual financial market data, demonstrating that it can allow us to answer different questions than the discrete approach can.

Recent years have seen a lot of work towards extending the established AGM belief revision theory with respect to iterating revision, preserving conditional beliefs, and handling sets of propositions as new information. In particular, novel postulates like independence and evidence retainment have been brought forth as new standards for revising epistemic states by (sets of) propositional information. In this paper, we propose a constructive approach for revising epistemic states by sets of (propositional and conditional) beliefs that combines ideas from nonmonotonic reasoning with conditional belief revision. We also propose a novel principle called enforcement that covers both independence and evidence retainment, and we show our revision operator to comply with major postulates from the literature. Moreover, we point out the relevance of our approach for default reasoning.

Temporal reasoning problems arise in many areas of AI, including planning, natural language understanding, and reasoning about physical systems. The computational complexity of continuous-time temporal constraint reasoning is fairly well understood. There are, however, many different cases where discrete time must be considered; various scheduling problems and reasoning about sampled physical systems are two examples. Here, the complexity of temporal reasoning is not as well-studied nor as well-understood. In order to get a better understanding, we consider the powerful Horn DLR formalism adapted for discrete time and study its computational complexity. We show that the full formalism is NP-hard and identify several maximal tractable subclasses. We also ‘lift’ the maximality results to obtain hardness results for other families of constraints. Finally, we discuss how the results and techniques presented in this paper can be used for studying even more expressive classes of temporal constraints.

The Boolean network is a mathematical model of biological systems, and has attracted much attention as a qualitative tool for analyzing the regulatory system. The stable states and dynamics of Boolean networks are characterized by their attractors, whose properties have been analyzed computationally, yet not much work has been done from the viewpoint of logical inference systems. In this paper, we show direct translations of Boolean networks into logic programs, and propose new methods to compute their trajectories and attractors based on inference on such logic programs. In particular, point attractors of both synchronous and asynchronous Boolean networks are characterized as supported models of logic programs so that SAT techniques can be applied to compute them. Investigation of these relationships suggests us to view Boolean networks as logic programs and vice versa.

We give a formal definition of generalized planning that is independent of any representation formalism. We assume that our generalized plans must work on a set of deterministic environments, which are essentially unrelated to each other. We prove that generalized planning for a finite set of environments is always decidable and EXPSPACE-complete. Our proof is constructive and gives us a sound, complete and complexity-wise optimal technique. We also consider infinite sets of environments, and show that generalized planning for the infinite "one-dimensional problems," known in the literature to be recursively enumerable when restricted to finite-state plans, is EXPSPACE-decidable without sequence functions, and solvable by generalized planning for finite sets.

Probabilistic logics which is followed by the development of the main methods that support reasoning with probability distributions, used in generalising probabilistic Boolean interaction, and, such as ProbLog, use an implicit definition finally, default logic is briefly discussed. We will use probabilistic of an interaction rule to combine probabilistic evidence Boolean interaction as a sound and generic, algebraic about atoms. In this paper, we show that way to combine uncertain evidence, whereas default this interaction rule is an example of a more general logic will be used as our language to implement the interaction class of interactions that can be described by nonmonotonic operators, again reflecting this double perspective on the logics. We furthermore show that such probabilistic logic. The new probabilistic logical framework local interactions about the probability of an atom is described in Section 3 and compared to other approaches can be described by convolution. The resulting extended in Section 4. The achievements of this research are reflected probabilistic logic supports nonmonotonic upon in Section 5. reasoning with probabilistic information.

The robot programming and plan language IndiGolog allows for on-line execution of actions and offline projections of programs in dynamic and partly unknown environments. Basic assumptions are that the outcomes of primitive and sensing actions are correctly modeled, and that the agent is informed about all exogenous events beyond its control. In real-world applications, however, such assumptions do not hold. In fact, an action’s outcome is error-prone and sensing results are noisy. In this paper, we present a belief management system in IndiGolog that is able to detect inconsistencies between a robot’s modeled belief and what happened in reality. The system furthermore derives explanations and maintains a consistent belief. Our main contributions are (1) a belief management system following a history-based diagnosis approach that allows an agent to actively cope with faulty actions and the occurrence of exogenous events; and (2) an implementation in IndiGolog and experimental results from a delivery domain.

We study a decidable fixpoint extension of temporal description logics. To this end we employ and extend decidability results obtained for various temporally first-order monodic extensions of (first-order) description logics. Using these techniques we obtain decidability and tight complexity results for various fixpoint extensions of temporal description logics.

In this paper we use the Kripke semantics characterization of Dummett logic to introduce a new way of handling non-forced formulas in tableau proof systems. We pursue the aim of reducing the search space by strictly increasing the number of forced propositional variables after the application of non-invertible rules. The focus of the paper is on a new tableau system for Dummett logic, for which we have an implementation.

We present a unifying approach to the efficient evaluation of propositional answer-set programs. Our approach is based on backdoors which are small sets of atoms that represent "clever reasoning shortcuts" through the search space. The concept of backdoors is widely used in the areas of propositional satisfiability and constraint satisfaction. We show how this concept can be adapted to the nonmonotonic setting and how it allows to augment various known tractable subproblems, such as the evaluation of Horn and acyclic programs. In order to use backdoors we need to find them first. We utilize recent advances in fixed-parameter algorithmics to detect small backdoors. This implies fixed-parameter tractability of the evaluation of propositional answer-set programs, parameterized by the size of backdoors. Hence backdoor size provides a structural parameter similar to the treewidth parameter previously considered. We show that backdoor size and treewidth are incomparable, hence there are instances that are hard for one and easy for the other parameter. We complement our theoretical results with first empirical results.