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Multi-agent reinforcement learning (MARL) is well-suited for runtime decision-making in optimizing the performance of systems where multiple agents coexist and compete for shared resources. However, applying common deep learning-based MARL solutions to real-world problems suffers from issues of interpretability, sample efficiency, partial observability, etc. To address these challenges, we present an event-driven formulation, where decision-making is handled by distributed co-operative MARL agents using neuro-symbolic methods. The recently introduced neuro-symbolic Logical Neural Networks (LNN) framework serves as a function approximator for the RL, to train a rules-based policy that is both logical and interpretable by construction. To enable decision-making under uncertainty and partial observability, we developed a novel probabilistic neuro-symbolic framework, Probabilistic Logical Neural Networks (PLNN), which combines the capabilities of logical reasoning with probabilistic graphical models. In PLNN, the upward/downward inference strategy, inherited from LNN, is coupled with belief bounds by setting the activation function for the logical operator associated with each neural network node to a probability-respecting generalization of the Fr\'echet inequalities. These PLNN nodes form the unifying element that combines probabilistic logic and Bayes Nets, permitting inference for variables with unobserved states. We demonstrate our contributions by addressing key MARL challenges for power sharing in a system-on-chip application.

Knowledge Base Question Answering (KBQA) tasks that involve complex reasoning are emerging as an important research direction. However, most existing KBQA datasets focus primarily on generic multi-hop reasoning over explicit facts, largely ignoring other reasoning types such as temporal, spatial, and taxonomic reasoning. In this paper, we present a benchmark dataset for temporal reasoning, TempQA-WD, to encourage research in extending the present approaches to target a more challenging set of complex reasoning tasks. Specifically, our benchmark is a temporal question answering dataset with the following advantages: (a) it is based on Wikidata, which is the most frequently curated, openly available knowledge base, (b) it includes intermediate sparql queries to facilitate the evaluation of semantic parsing based approaches for KBQA, and (c) it generalizes to multiple knowledge bases: Freebase and Wikidata. The TempQA-WD dataset is available at https://github.com/IBM/tempqa-wd., Comment: 7 pages, 2 figures, 7 tables. arXiv admin note: substantial text overlap with arXiv:2109.13430

Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from fuzzy or real-valued logic that are parameter-free thus diminishing their capacity to fit the data, other approaches are only loosely based on logic making it difficult to interpret the learned "rules". In this paper, we propose learning rules with the recently proposed logical neural networks (LNN). Compared to others, LNNs offer strong connection to classical Boolean logic thus allowing for precise interpretation of learned rules while harboring parameters that can be trained with gradient-based optimization to effectively fit the data. We extend LNNs to induce rules in first-order logic. Our experiments on standard benchmarking tasks confirm that LNN rules are highly interpretable and can achieve comparable or higher accuracy due to their flexible parameterization.

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds of logic formulas, this logic specifies a set of probability distributions over all interpretations. On the one hand, our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. On the other hand, it has a Markov condition similar to Bayesian networks and Markov random fields that is critical in real-world applications. Having both these properties makes this logic unique, and we investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud. The results show that the proposed method outperforms existing approaches, and its advantage lies in aggregating multiple sources of imprecise information.

Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential variables. Recent work of query embeddings provides fast querying, but most approaches model set logic with closed regions, so lack negation. Query embeddings that do support negation use densities that suffer drawbacks: 1) only improvise logic, 2) use expensive distributions, and 3) poorly model answer uncertainty. In this paper, we propose Logic Embeddings, a new approach to embedding complex queries that uses Skolemisation to eliminate existential variables for efficient querying. It supports negation, but improves on density approaches: 1) integrates well-studied t-norm logic and directly evaluates satisfiability, 2) simplifies modeling with truth values, and 3) models uncertainty with truth bounds. Logic Embeddings are competitively fast and accurate in query answering over large, incomplete knowledge graphs, outperform on negation queries, and in particular, provide improved modeling of answer uncertainty as evidenced by a superior correlation between answer set size and embedding entropy., Comment: IBM Research

Knowledge base question answering (KBQA)is an important task in Natural Language Processing. Existing approaches face significant challenges including complex question understanding, necessity for reasoning, and lack of large end-to-end training datasets. In this work, we propose Neuro-Symbolic Question Answering (NSQA), a modular KBQA system, that leverages (1) Abstract Meaning Representation (AMR) parses for task-independent question understanding; (2) a simple yet effective graph transformation approach to convert AMR parses into candidate logical queries that are aligned to the KB; (3) a pipeline-based approach which integrates multiple, reusable modules that are trained specifically for their individual tasks (semantic parser, entity andrelationship linkers, and neuro-symbolic reasoner) and do not require end-to-end training data. NSQA achieves state-of-the-art performance on two prominent KBQA datasets based on DBpedia (QALD-9 and LC-QuAD1.0). Furthermore, our analysis emphasizes that AMR is a powerful tool for KBQA systems., Comment: Accepted to Findings of ACL

Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of such systems. We give a sound and strongly complete axiomatization that can be parametrized to cover essentially every real-valued logic, including all the common fuzzy logics. Our class of sentences are very rich, and each describes a set of possible real values for a collection of formulas of the real-valued logic, including which combinations of real values are possible. Strong completeness allows us to derive exactly what information can be inferred about the combinations of real values of a collection of formulas given information about the combinations of real values of several other collections of formulas. We then extend the axiomatization to deal with weighted subformulas. Finally, we give a decision procedure based on linear programming for deciding, for certain real-valued logics and under certain natural assumptions, whether a set of our sentences logically implies another of our sentences., Comment: 12 pages (incl. references). To be submitted to PNAS

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge., Comment: 10 pages (incl. references), 38 pages supplementary, 7 figures, 9 tables, 6 algorithms. In submission to NeurIPS 2020

We conduct a pilot investigation to determine the optimal combination of color and variability information to identify quasars in current and future multi-epoch optical surveys. We use a Bayesian quasar selection algorithm (Richards et al. 2004) to identify 35,820 type 1 quasar candidates in a 239 square degree field of the Sloan Digital Sky Survey (SDSS) Stripe 82, using a combination of optical photometry and variability. Color analysis is performed on 5-band single- and multi-epoch SDSS optical photometry to a depth of r ~22.4. From these data, variability parameters are calculated by fitting the structure function of each object in each band with a power law model using 10 to >100 observations over timescales from ~1 day to ~8 years. Selection was based on a training sample of 13,221 spectroscopically-confirmed type-1 quasars, largely from the SDSS. Using variability alone, colors alone, and combining variability and colors we achieve 91%, 93%, and 97% quasar completeness and 98%, 98%, and 97% efficiency respectively, with particular improvement in the selection of quasars at 2.7

We identify 885,503 type 1 quasar candidates to i<22 using the combination of optical and mid-IR photometry. Optical photometry is taken from the Sloan Digital Sky Survey-III: Baryon Oscillation Spectroscopic Survey (SDSS-III/BOSS), while mid-IR photometry comes from a combination of data from the Wide-Field Infrared Survey Explorer (WISE) "ALLWISE" data release and several large-area Spitzer Space Telescope fields. Selection is based on a Bayesian kernel density algorithm with a training sample of 157,701 spectroscopically-confirmed type-1 quasars with both optical and mid-IR data. Of the quasar candidates, 733,713 lack spectroscopic confirmation (and 305,623 are objects that we have not previously classified as photometric quasar candidates). These candidates include 7874 objects targeted as high probability potential quasars with 3.53.5 than the traditional mid-IR selection "wedges" and to 2.23. This catalog paves the way for luminosity-dependent clustering investigations of large numbers of faint, high-redshift quasars and for further machine learning quasar selection using Spitzer and WISE data combined with other large-area optical imaging surveys., Comment: 54 pages, 17 figures; accepted by ApJS Data for tables 1 and 2 available at http://www.physics.drexel.edu/~gtr/outgoing/optirqsos/data/master_quasar_catalogs.011414.fits.bz2 and http://www.physics.drexel.edu/~gtr/outgoing/optirqsos/data/optical_ir_quasar_candidates.052015.fits.bz2

We present a catalog of 1,172,157 quasar candidates selected from the photometric imaging data of the Sloan Digital Sky Survey (SDSS). The objects are all point sources to a limiting magnitude of i=21.3 from 8417 sq. deg. of imaging from SDSS Data Release 6 (DR6). This sample extends our previous catalog by using the latest SDSS public release data and probing both UV-excess and high-redshift quasars. While the addition of high-redshift candidates reduces the overall efficiency (quasars:quasar candidates) of the catalog to ~80%, it is expected to contain no fewer than 850,000 bona fide quasars -- ~8 times the number of our previous sample, and ~10 times the size of the largest spectroscopic quasar catalog. Cross-matching between our photometric catalog and spectroscopic quasar catalogs from both the SDSS and 2dF Surveys, yields 88,879 spectroscopically confirmed quasars. For judicious selection of the most robust UV-excess sources (~500,000 objects in all), the efficiency is nearly 97% -- more than sufficient for detailed statistical analyses. The catalog's completeness to type 1 (broad-line) quasars is expected to be no worse than 70%, with most missing objects occurring at z<0.7 and 2.5