This paper addresses the topic of semantic world modeling by conjoining probabilistic reasoning and object anchoring. The proposed approach uses a so-called bottom-up object anchoring method that relies on rich continuous attribute values measured from perceptual sensor data. A novel anchoring matching function learns to maintain object entities in space and time and is validated using a large set of trained humanly annotated ground truth data of real-world objects. For more complex scenarios, a high-level probabilistic object tracker has been integrated with the anchoring framework and handles the tracking of occluded objects via reasoning about the state of unobserved objects. We demonstrate the performance of our integrated approach through scenarios such as the shell game scenario, where we illustrate how anchored objects are retained by preserving relations through probabilistic reasoning.

Weighted model counting has recently been extended to weighted model integration, which can be used to solve hybrid probabilistic reasoning problems. Such problems involve both discrete and continuous probability distributions. We show how standard knowledge compilation techniques (to SDDs and d-DNNFs) apply to weighted model integration, and use it in two novel solvers, one exact and one approximate solver. Furthermore, we extend the class of employable weight functions to actual probability density functions instead of mere polynomial weight functions.

Weighted Model Integration (WMI) is a popular technique for probabilistic inference that extends Weighted Model Counting (WMC) -- the standard inference technique for inference in discrete domains -- to domains with both discrete and continuous variables.  However, existing WMI solvers each have different interfaces and use different formats for representing WMI problems.  Therefore, we introduce pywmi (http://pywmi.org), an open source framework and toolbox for probabilistic inference using WMI, to address these shortcomings.  Crucially, pywmi fixes a common internal format for WMI problems and introduces a common interface for WMI solvers.  To assist users in modeling WMI problems, pywmi introduces modeling languages based on SMT-LIB.v2 or MiniZinc and parsers for both.  To assist users in comparing WMI solvers, pywmi includes implementations of several state-of-the-art solvers, a fast approximate WMI solver, and a command-line interface to solve WMI problems.  Finally, to assist developers in implementing new solvers, pywmi provides Python implementations of commonly used subroutines.

Robotic agents should be able to learn from sub-symbolic sensor data and, at the same time, be able to reason about objects and communicate with humans on a symbolic level. This raises the question of how to overcome the gap between symbolic and sub-symbolic artificial intelligence. We propose a semantic world modeling approach based on bottom-up object anchoring using an object-centered representation of the world. Perceptual anchoring processes continuous perceptual sensor data and maintains a correspondence to a symbolic representation. We extend the definitions of anchoring to handle multi-modal probability distributions and we couple the resulting symbol anchoring system to a probabilistic logic reasoner for performing inference. Furthermore, we use statistical relational learning to enable the anchoring framework to learn symbolic knowledge in the form of a set of probabilistic logic rules of the world from noisy and sub-symbolic sensor input. The resulting framework, which combines perceptual anchoring and statistical relational learning, is able to maintain a semantic world model of all the objects that have been perceived over time, while still exploiting the expressiveness of logical rules to reason about the state of objects which are not directly observed through sensory input data. To validate our approach we demonstrate, on the one hand, the ability of our system to perform probabilistic reasoning over multi-modal probability distributions, and on the other hand, the learning of probabilistic logical rules from anchored objects produced by perceptual observations. The learned logical rules are, subsequently, used to assess our proposed probabilistic anchoring procedure. We demonstrate our system in a setting involving object interactions where object occlusions arise and where probabilistic inference is needed to correctly anchor objects.

Real world decision making problems often involve both discrete and continuous variables and require a combination of probabilistic and deterministic knowledge. Stimulated by recent advances in automated reasoning technology, hybrid (discrete+continuous) probabilistic reasoning with constraints has emerged as a lively and fast growing research field. In this paper we provide a survey of existing techniques for hybrid probabilistic inference with logic and algebraic constraints. We leverage weighted model integration as a unifying formalism and discuss the different paradigms that have been used as well as the expressivity-efficiency trade-offs that have been investigated. We conclude the survey with a comparative overview of existing implementations and a critical discussion of open challenges and promising research directions.