Related papers: Algebraic Semantics of Datalog with Equality
Recent advances in Large Language Models (LLMs) are fostering their integration into several reasoning-related fields, including Automated Planning (AP). However, their integration into Hierarchical Planning (HP), a subfield of AP that…
This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and quantitative…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
Retrieval-Augmented Generation (RAG) grounds large language models in external evidence, yet it still falters when answers must be pieced together across semantically distant documents. We close this gap with the Hierarchical Lexical Graph…
Inductive Logic Programming (ILP) combines rule-based and statistical artificial intelligence methods, by learning a hypothesis comprising a set of rules given background knowledge and constraints for the search space. We focus on extending…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using…
The traditional approach in HEP analysis software is to loop over every event and every object via the ROOT framework. This method follows an imperative paradigm, in which the code is tied to the storage format and steps of execution. A…
Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming…
Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…
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…
Conversational human-likeness plays a central role in human-AI interaction, yet it has remained difficult to define, measure, and optimize. As a result, improvements in human-like behavior are largely driven by scale or broad supervised…
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…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…