Related papers: INDUCTION: Finite-Structure Concept Synthesis in F…
We prove a criterion that allows to construct units in product systems of correspondences with prescribed infinitesimal characterizations. This criterion summarizes proofs of known results and new applications. It also frees the hypothesis…
In this paper we propose a general framework to integrate supervised and unsupervised examples with background knowledge expressed by a collection of first-order logic clauses into kernel machines. In particular, we consider a multi-task…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Large language models achieve strong performance on many tasks, but their training makes it hard to see which properties of the input support efficient linguistic rule learning. We ask how three cognitively-inspired principles of input…
In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…
In this paper, we propose a first-order ontology for generalized stratified order structure. We then classify the models of the theory using model-theoretic techniques. An ontology mapping from this ontology to the core theory of Process…
Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global section functor) instead of general gluing. The sconing is…
Large Language Models (LLMs) exhibit impressive performance across various domains but still struggle with arithmetic reasoning tasks. Recent work shows the effectiveness of prompt design methods in enhancing reasoning capabilities.…
The ability of Large Language Models (LLMs) to generate structured outputs that follow arbitrary schemas is crucial to a wide range of downstream tasks that require diverse structured representations of results such as information…
This paper describes the first-order logical environment FOLE. Institutions in general, and logical environments in particular, give equivalent heterogeneous and homogeneous representations for logical systems. As such, they offer a…
Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries as well as first-order knowledge compilation (FOKC) based on weighted model counting. To…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Unsupervised learning objectives like autoregressive and masked language modeling constitute a significant part in producing pre-trained representations that perform various downstream applications from natural language understanding to…
Data-to-text generation involves transforming structured data, often represented as predicate-argument tuples, into coherent textual descriptions. Despite recent advances, systems still struggle when confronted with unseen combinations of…
We investigate here concept learning from incomplete examples. Our first purpose is to discuss to what extent logical learning settings have to be modified in order to cope with data incompleteness. More precisely we are interested in…
Instruction-tuned large language models have shown remarkable performance in aligning generated text with user intentions across various tasks. However, maintaining human-like discourse structure in the generated text remains a challenging…
Large language models are able to perform a task by conditioning on a few input-output demonstrations - a paradigm known as in-context learning. We show that language models can explicitly infer an underlying task from a few demonstrations…
Prompt optimization has become crucial for enhancing the performance of large language models (LLMs) across a broad range of tasks. Although many research papers demonstrate its effectiveness, practical adoption is hindered because existing…
Large language models (LLMs) have demonstrated strong performance in a wide-range of language tasks without requiring task-specific fine-tuning. However, they remain prone to hallucinations and inconsistencies, and often struggle with…
This paper introduces Formula Prompting (FP) and Formula-One Prompting (F-1), two single-call methods that elicit governing equations before solving applied-math problems. Chain-of-Thought (CoT) and Program-of-Thought (PoT) prompting…