Related papers: On the Semantic Relationship between Probabilistic…
A Markov logic network (MLN) $\mathbb{M}$ determines a probability distribution $\mathbb{P}_n^\mathbb{M}$ on the set $\mathbf{W}_n$ of structures, or ``possible worlds'', with domain $\{1, \ldots, n\}$. We study the properties of such…
Markov Logic Networks (MLNs) have emerged as a powerful framework that combines statistical and logical reasoning; they have been applied to many data intensive problems including information extraction, entity resolution, and text mining.…
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as…
By incorporating the methods of Answer Set Programming (ASP) and Markov Logic Networks (MLN), LPMLN becomes a powerful tool for non-monotonic, inconsistent and uncertain knowledge representation and reasoning. To facilitate the applications…
Machine learning is rapidly making its pathway across all of the natural sciences, including physical sciences. The rate at which ML is impacting non-scientific disciplines is incomparable to that in the physical sciences. This is partly…
Complex, non-additive genetic interactions are common and can be critical in determining phenotypes. Genome-wide association studies (GWAS) and similar statistical studies of linkage data, however, assume additive models of gene…
Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer…
LPMLN is a powerful knowledge representation and reasoning tool that combines the non-monotonic reasoning ability of Answer Set Programming (ASP) and the probabilistic reasoning ability of Markov Logic Networks (MLN). In this paper, we…
Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation…
We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is…
We present $\mathcal{MEL}^{++}$ (M denotes Markov logic networks) an extension of the log-linear description logics $\mathcal{EL}^{++}$-LL with concrete domains, nominals, and instances. We use Markov logic networks (MLNs) in order to find…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Despite the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for random variables whose distributions combine discrete and continuous elements. We develop the notion of…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
Softmax Loss (SL) is widely applied in recommender systems (RS) and has demonstrated effectiveness. This work analyzes SL from a pairwise perspective, revealing two significant limitations: 1) the relationship between SL and conventional…