Related papers: On Knowledge Compilation For Two-Variable First-Or…
The importance of taking individual, potentially conflicting perspectives into account when dealing with knowledge has been widely recognised. Many existing ontology management approaches fully merge knowledge perspectives, which may…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
In this paper we study the role of cliquewidth in succinct representation of Boolean functions. Our main statement is the following: Let $Z$ be a Boolean circuit having cliquewidth $k$. Then there is another circuit $Z^*$ computing the same…
Question answering models struggle to generalize to novel compositions of training patterns, such to longer sequences or more complex test structures. Current end-to-end models learn a flat input embedding which can lose input syntax…
The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. The boundary between fragments for which WFOMC can be computed in polynomial time…
Recent studies have shown that sequence-to-sequence (seq2seq) models struggle with compositional generalization (CG), i.e., the ability to systematically generalize to unseen compositions of seen components. There is mounting evidence that…
With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for…
Chain of Thought (CoT) prompting can encourage language models to engage in multi-step logical reasoning. The quality of the provided demonstrations significantly influences the success of downstream inference tasks. Current unsupervised…
This study investigates an explainable reasoning method for financial decision-making based on knowledge-enhanced large language model agents. To address the limitations of traditional financial decision methods that rely on parameterized…
The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…
This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…
We provide a decidable characterization of regular forest languages definable in FO2(<h,<v). By FO2(<h,<v) we refer to the two variable fragment of first order logic built from the descendant relation and the following sibling relation. In…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
Relational reasoning lies at the core of many NLP tasks, drawing on complementary signals from text and graphs. While prior research has investigated how to leverage this dual complementarity, a detailed and systematic understanding of…
Pretrained language models can encode a large amount of knowledge and utilize it for various reasoning tasks, yet they can still struggle to learn novel factual knowledge effectively from finetuning on limited textual demonstrations. In…
Large Language Models (LLMs) trained on petabytes of data are highly compressed repositories of a significant proportion of the knowledge accumulated and distilled so far. In this paper we study techniques to elicit this knowledge in the…
Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
Reasoning-capable language models achieve state-of-the-art performance in diverse complex tasks by generating long, explicit Chain-of-Thought (CoT) traces. While recent works show that base models can acquire such reasoning traces via…
In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…