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Answer Set Programming (ASP) is a prominent problem-modeling and solving framework, whose solutions are called answer sets. Epistemic logic programs (ELP) extend ASP to reason about all or some answer sets. Solutions to an ELP can be seen…

We propose Posterior Bootstrap, a set of algorithms extending Weighted Likelihood Bootstrap, to properly incorporate prior information and address the problem of model misspecification in Bayesian inference. We consider two approaches to…

While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…

Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming (ASP). While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive…

This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random…

In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to specify the probability structure. We consider the case in which probabilistic…

Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…

Probabilistic logic reasoning is a central component of such cognitive architectures as OpenCog. However, as an integrative architecture, OpenCog facilitates cognitive synergy via hybridization of different inference methods. In this paper,…

One important challenge for probabilistic logics is reasoning with very large knowledge bases (KBs) of imperfect information, such as those produced by modern web-scale information extraction systems. One scalability problem shared by many…

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this we use the two different mathematical tools of Propositional Logic and…

Model uncertainty is pervasive in real world analysis situations and is an often-neglected issue in applied statistics. However, standard approaches to the research process do not address the inherent uncertainty in model building and,…

Recent years have seen a surge of interest in Probabilistic Logic Programming (PLP) and Statistical Relational Learning (SRL) models that combine logic with probabilities. Structure learning of these systems is an intersection area of…

This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing…

A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…

This research explores the integration of large language models (LLMs) into scientific data assimilation, focusing on combustion science as a case study. Leveraging foundational models integrated with Retrieval-Augmented Generation (RAG)…

The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are…

In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…

Answer set programming (ASP) aims to realize the AI vision: The user specifies the problem, and the computer solves it. Indeed, ASP has made this vision true in many application domains. However, will current ASP solving techniques scale up…

Probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting…