Direct design of ground-state probabilistic logic using many-body interactions for probabilistic computing.

In this work, an innovative design model aimed at enhancing the efficacy of ground-state probabilistic logic with a binary energy landscape (GSPL-BEL) is presented. This model enables the direct conversion of conventional CMOS-based logic circuits into corresponding probabilistic graphical representations based on a given truth table. Compared to the conventional approach of solving the configuration of Ising model-basic probabilistic gates through linear programming, our model directly provides configuration parameters with embedded many-body interactions. For larger-scale probabilistic logic circuits, the GSPL-BEL model can fully utilize the dimensions of many-body interactions, achieving minimal node overhead while ensuring the simplest binary energy landscape and circumventing additional logic synthesis steps. To validate its effectiveness, hardware implementations of probabilistic logic gates were conducted. Probabilistic bits were introduced as Ising cells, and cascaded conventional XNOR gates along with passive resistor networks were precisely designed to realize many-body interactions. HSPICE circuit simulation results demonstrate that the probabilistic logic circuits designed based on this model can successfully operate in free, forward, and reverse modes, exhibiting the simplest binary probability distributions. For a 2-bit × 2-bit integer factorizer involving many-body interactions, compared to the logic synthesis approach, the GSPL-BEL model significantly reduces the number of consumed nodes, the solution space (in the free-run mode), and the number of energy levels from 12, 4096, and 9-8, 256, and 2, respectively. Our findings demonstrate the significant potential of the GSPL-BEL model in optimizing the structure and performance of probabilistic logic circuits, offering a new robust tool for the design and implementation of future probabilistic computing systems.

Neural-Symbolic Ensemble Learning for early-stage prediction of critical state of Covid-19 patients.

Recently, Artificial Intelligence (AI) and Machine Learning (ML) have been successfully applied to many domains of interest including medical diagnosis. Due to the availability of a large quantity of data, it is possible to build reliable AI systems that assist humans in making decisions. The recent Covid-19 pandemic quickly spread over the world causing serious health problems and severe economic and social damage. Computer scientists are actively working together with doctors on different ML models to diagnose Covid-19 patients using Computed Tomography (CT) scans and clinical data. In this work, we propose a neural-symbolic system that predicts if a Covid-19 patient arriving at the hospital will end in a critical condition. The proposed system relies on Deep 3D Convolutional Neural Networks (3D-CNNs) for analyzing lung CT scans of Covid-19 patients, Decision Trees (DTs) for predicting if a Covid-19 patient will eventually pass away by analyzing its clinical data, and a neural system that integrates the previous ones using Hierarchical Probabilistic Logic Programs (HPLPs). Predicting if a Covid-19 patient will end in a critical condition is useful for managing the limited number of intensive care at the hospital. Moreover, knowing early that a Covid-19 patient could end in serious conditions allows doctors to gain early knowledge on patients and provide special treatment to those predicted to finish in critical conditions. The proposed system, entitled Neural HPLP, obtains good performance in terms of area under the receiver operating characteristic and precision curves with values of about 0.96 for both metrics. Therefore, with Neural HPLP, it is possible not only to efficiently predict if Covid-19 patients will end in severe conditions but also possible to provide an explanation of the prediction. This makes Neural HPLP explainable, interpretable, and reliable. Graphical abstract Representation of Neural HPLP. From top to bottom, the two different types of data collected from the same patient and used in this project are represented. This data feeds the two different machine learning systems and the integration of the two systems using Hierarchical Probabilistic Logic Program.

Functional gradients in the human lateral prefrontal cortex revealed by a comprehensive coordinate-based meta-analysis.

The lateral prefrontal cortex (LPFC) of humans enables flexible goal-directed behavior. However, its functional organization remains actively debated after decades of research. Moreover, recent efforts aiming to map the LPFC through meta-analysis are limited, either in scope or in the inferred specificity of structure-function associations. These limitations are in part due to the limited expressiveness of commonly-used data analysis tools, which restricts the breadth and complexity of questions that can be expressed in a meta-analysis. Here, we adopt NeuroLang, a novel approach to more expressive meta-analysis based on probabilistic first-order logic programming, to infer the organizing principles of the LPFC from 14,371 neuroimaging studies. Our findings reveal a rostrocaudal and a dorsoventral gradient, respectively explaining the most and second most variance in meta-analytic connectivity across the LPFC. Moreover, we identify a unimodal-to-transmodal spectrum of coactivation patterns along with a concrete-to-abstract axis of structure-function associations extending from caudal to rostral regions of the LPFC. Finally, we infer inter-hemispheric asymmetries along the principal rostrocaudal gradient, identifying hemisphere-specific associations with topics of language, memory, response inhibition, and sensory processing. Overall, this study provides a comprehensive meta-analytic mapping of the LPFC, grounding future hypothesis generation on a quantitative overview of past findings.

Intention Recognition With ProbLog.

In many scenarios where robots or autonomous systems may be deployed, the capacity to infer and reason about the intentions of other agents can improve the performance or utility of the system. For example, a smart home or assisted living facility is better able to select assistive services to deploy if it understands the goals of the occupants in advance. In this article, we present a framework for reasoning about intentions using probabilistic logic programming. We employ ProbLog, a probabilistic extension to Prolog, to infer the most probable intention given observations of the actions of the agent and sensor readings of important aspects of the environment. We evaluated our model on a domain modeling a smart home. The model achieved 0.75 accuracy at full observability. The model was robust to reduced observability.

Adapting Logic to Physics: The Quantum-Like Eigenlogic Program.

Considering links between logic and physics is important because of the fast development of quantum information technologies in our everyday life. This paper discusses a new method in logic inspired from quantum theory using operators, named Eigenlogic. It expresses logical propositions using linear algebra. Logical functions are represented by operators and logical truth tables correspond to the eigenvalue structure. It extends the possibilities of classical logic by changing the semantics from the Boolean binary alphabet { 0 , 1 } using projection operators to the binary alphabet { + 1 , - 1 } employing reversible involution operators. Also, many-valued logical operators are synthesized, for whatever alphabet, using operator methods based on Lagrange interpolation and on the Cayley-Hamilton theorem. Considering a superposition of logical input states one gets a fuzzy logic representation where the fuzzy membership function is the quantum probability given by the Born rule. Historical parallels from Boole, Post, Poincaré and Combinatory Logic are presented in relation to probability theory, non-commutative quaternion algebra and Turing machines. An extension to first order logic is proposed inspired by Grover's algorithm. Eigenlogic is essentially a logic of operators and its truth-table logical semantics is provided by the eigenvalue structure which is shown to be related to the universality of logical quantum gates, a fundamental role being played by non-commutativity and entanglement.

LogicNet: probabilistic continuous logics in reconstructing gene regulatory networks.

BACKGROUND: Gene Regulatory Networks (GRNs) have been previously studied by using Boolean/multi-state logics. While the gene expression values are usually scaled into the range [0, 1], these GRN inference methods apply a threshold to discretize the data, resulting in missing information. Most of studies apply fuzzy logics to infer the logical gene-gene interactions from continuous data. However, all these approaches require an a priori known network structure. RESULTS: Here, by introducing a new probabilistic logic for continuous data, we propose a novel logic-based approach (called the LogicNet) for the simultaneous reconstruction of the GRN structure and identification of the logics among the regulatory genes, from the continuous gene expression data. In contrast to the previous approaches, the LogicNet does not require an a priori known network structure to infer the logics. The proposed probabilistic logic is superior to the existing fuzzy logics and is more relevant to the biological contexts than the fuzzy logics. The performance of the LogicNet is superior to that of several Mutual Information-based and regression-based tools for reconstructing GRNs. CONCLUSIONS: The LogicNet reconstructs GRNs and logic functions without requiring prior knowledge of the network structure. Moreover, in another application, the LogicNet can be applied for logic function detection from the known regulatory genes-target interactions. We also conclude that computational modeling of the logical interactions among the regulatory genes significantly improves the GRN reconstruction accuracy.

Symbolic Learning and Reasoning With Noisy Data for Probabilistic Anchoring.

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.

Neural-Symbolic Argumentation Mining: An Argument in Favor of Deep Learning and Reasoning.

Deep learning is bringing remarkable contributions to the field of argumentation mining, but the existing approaches still need to fill the gap toward performing advanced reasoning tasks. In this position paper, we posit that neural-symbolic and statistical relational learning could play a crucial role in the integration of symbolic and sub-symbolic methods to achieve this goal.

Probabilistic-Input, Noisy Conjunctive Models for Cognitive Diagnosis.

Existing cognitive diagnosis models conceptualize attribute mastery status discretely as either mastery or non-mastery. This study proposes a different conceptualization of attribute mastery as a probabilistic concept, i.e., the probability of mastering a specific attribute for a person, and developing a probabilistic-input, noisy conjunctive (PINC) model, in which the probability of mastering an attribute for a person is a parameter to be estimated from data. And a higher-order version of the PINC model is used to consider the associations among attributes. The results of simulation studies revealed a good parameter recovery for the new models using the Bayesian method. The Examination for the Certificate of Proficiency in English (ECPE) data set was analyzed to illustrate the implications and applications of the proposed models. The results indicated that PINC models had better model-data fit, smaller item parameter estimates, and more refined estimates of attribute mastery.

A Probabilistic Finite State Logic Machine Realized Experimentally on a Single Dopant Atom.

Exploiting the potential of nanoscale devices for logic processing requires the implementation of computing functionalities departing from the conventional switching paradigm. We report on the design and the experimental realization of a probabilistic finite state machine in a single phosphorus donor atom placed in a silicon matrix electrically addressed and probed by scanning tunneling spectroscopy (STS). The single atom logic unit simulates the flow of visitors in a maze whose topology is determined by the dynamics of the electronic transport through the states of the dopant. By considering the simplest case of a unique charge state for which three electronic states can be resolved, we demonstrate an efficient solution of the following problem: in a maze of four connected rooms, what is the optimal combination of door opening rates in order to maximize the time that visitors spend in one specific chamber? The implementation takes advantage of the stochastic nature of electron tunneling, while the output remains the macroscopic current whose reading can be realized with standard techniques and does not require single electron sensitivity.

Stochastic analysis of Chemical Reaction Networks using Linear Noise Approximation.

Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.

Describing disease processes using a probabilistic logic of qualitative time.

BACKGROUND: Clinical knowledge about progress of diseases is characterised by temporal information as well as uncertainty. However, precise timing information is often unavailable in medicine. In previous research this problem has been tackled using Allen's qualitative algebra of time, which, despite successful medical application, does not deal with the associated uncertainty. OBJECTIVES: It is investigated whether and how Allen's temporal algebra can be extended to handle uncertainty to better fit available knowledge and data of disease processes. METHODS: To bridge the gap between probability theory and qualitative time reasoning, methods from probabilistic logic are explored. The relation between the probabilistic logic representation and dynamic Bayesian networks is analysed. By studying a typical, and clinically relevant problem, the detection of exacerbations of chronic obstructive pulmonary disease (COPD), it is determined whether the developed probabilistic logic of qualitative time is medically useful. RESULTS: The probabilistic logic extension of Allen's temporal algebra, called Qualitative Time CP-logic provides a tool to model disease processes at a natural level of abstraction and is sufficiently powerful to reason with imprecise, uncertain knowledge. The representation of the COPD disease process gives evidence that the framework can be applied functionally to a clinical problem. CONCLUSION: The combination of qualitative time and probabilistic logic offers a useful framework for modelling knowledge and data to describe disease processes in clinical medicine.