Related papers: Parametric Connectives in Disjunctive Logic Progra…

Large Language Models have been found to create plans that are neither executable nor verifiable in grounded environments. An emerging line of work demonstrates success in using the LLM as a formalizer to generate a formal representation of…

Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which…

Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens…

On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single…

Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of…

Integrating large language models (LLMs) with knowledge graphs derived from domain-specific data represents an important advancement towards more powerful and factual reasoning. As these models grow more capable, it is crucial to enable…

The massive computational costs of scaling modern deep learning architectures have driven the widespread use of parameter-efficient low-rank structures, such as LoRA and low-rank factorization. However, theoretical guarantees for their…

We present a new Deep Dictionary Learning and Coding Network (DDLCN) for image recognition tasks with limited data. The proposed DDLCN has most of the standard deep learning layers (e.g., input/output, pooling, fully connected, etc.), but…

Large Language Models (LLMs) excel at intuitive, implicit reasoning. Guiding LLMs to construct thought chains can enhance their deliberate reasoning abilities, but also faces challenges such as hallucination. Knowledge Graphs (KGs) can…

Large language models (LLMs) are able to generate human-like responses to user queries. However, LLMs exhibit inherent limitations, especially because they hallucinate. This paper introduces LP-LM, a system that grounds answers to questions…

This paper presents a logic language for expressing NP search and optimization problems. Specifically, first a language obtained by extending (positive) Datalog with intuitive and efficient constructs (namely, stratified negation,…

Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types.…

To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an…

Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…

Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-free logic program encoding the problem itself. Several…

Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an…

Grassroots Logic Programs (GLP) is a concurrent logic programming language in which logic variables are partitioned into paired readers and writers. An assignment is produced at most once via a writer and consumed at most once via its…

Improving the multi-step reasoning ability of Large Language Models (LLMs) is a critical yet challenging task. The dominant paradigm, outcome-supervised reinforcement learning (RLVR), rewards only correct final answers, often propagating…