Related papers: Representing Isabelle in LF
Inductive reasoning is an essential capability for large language models (LLMs) to achieve higher intelligence, which requires the model to generalize rules from observed facts and then apply them to unseen examples. We present MIRAGE, a…
We study some non-semisimple representations of affine Temperley--Lieb algebras and related cellular algebras. In particular, we classify extensions between simple standard modules. Moreover, we construct a completion which is an infinite…
The development of large language models (LLMs) is limited by a lack of explainability, the absence of a unifying theory, and prohibitive operational costs. We propose a neuro-theoretical framework for the emergence of intelligence in…
Linguistic typology aims to capture structural and semantic variation across the world's languages. A large-scale typology could provide excellent guidance for multilingual Natural Language Processing (NLP), particularly for languages that…
Modern functional-logic programming languages like Toy or Curry feature non-strict non-deterministic functions that behave under call-time choice semantics. A standard formulation for this semantics is the CRWL logic, that specifies a proof…
Logical frameworks are successful in modeling proof systems. Recently, CoLF extended the logical framework LF to support higher-order rational terms that enable adequate encoding of circular objects and derivations. In this paper, we…
The development of Large Language Models (LLMs) provides human-centered Artificial General Intelligence (AGI) with a glimmer of hope. Empathy serves as a key emotional attribute of humanity, playing an irreplaceable role in human-centered…
Large language models (LLMs) exhibit emergent behaviors suggestive of human-like reasoning. While recent work has identified structured conceptual representations within these models, it remains unclear whether they functionally rely on…
We introduce a modular prompting framework that supports safer and more adaptive use of large language models (LLMs) across dynamic, user-centered tasks. Grounded in human learning theory, particularly the Zone of Proximal Development…
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…
Large Language Models (LLMs) excel at understanding natural language but struggle with explicit commonsense reasoning. A recent trend of research suggests that the combination of LLM with robust symbolic reasoning systems can overcome this…
In the hardware design process, hardware components are usually described in a hardware description language. Most of the hardware description languages, such as Verilog and VHDL, do not have mathematical foundation and hence are not fit…
The major concern in the study of categories of logics is to describe condition for preservation, under the a method of combination of logics, of meta-logical properties. Our complementary approach to this field is study the "global"…
This paper introduces WOLF, a C++ estimation framework based on factor graphs and targeted at mobile robotics. WOLF can be used beyond SLAM to handle self-calibration, model identification, or the observation of dynamic quantities other…
Recent studies empirically indicate that language models (LMs) encode rich world knowledge beyond mere semantics, attracting significant attention across various fields. However, in the recommendation domain, it remains uncertain whether…
We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an…
Language Models (LMs) have demonstrated impressive capabilities in solving complex reasoning tasks, particularly when prompted to generate intermediate explanations. However, it remains an open question whether these intermediate reasoning…
Although contemporary model theory has been called "algebraic geometry minus fields", the formal methods of the two fields are radically different. This dissertation aims to shrink that gap by presenting a theory of logical schemes,…
We investigate the extent to which Linear Temporal Logic (LTL) formulas can be uniquely characterized by a finite set of labeled examples. We consider different types of examples, ranging from finite words to transfinite words, as well as…
We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…