Related papers: A tree rewriting system for the Reflection Calculu…
We study strictly positive logics in the language $\mathscr{L}^+$, which constructs formulas from $\top$, propositional variables, conjunction, and diamond modalities. We begin with the base system $\bf K^+$, the strictly positive fragment…
Strictly positive logics recently attracted attention both in the description logic and in the provability logic communities for their combination of efficiency and sufficient expressivity. The language of Reflection Calculus RC consists of…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…
Generative Recommendation (GR) has become a promising paradigm for large-scale recommendation systems. However, existing GR models typically perform single-pass decoding without explicit refinement, causing early deviations to accumulate…
We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses…
Multi-step reasoning remains a key challenge for Large Language Models (LLMs), particularly in complex domains such as mathematics and creative writing. While recent approaches including ReAct, Reflexion, and Self-Refine improve reasoning…
Tree search methods have demonstrated impressive performance in code generation. Previous methods combine tree search with reflection that summarizes past mistakes to achieve iterative improvement. However, these methods face significant…
Recent advancements in Large Language Models (LLMs) have expanded the horizons of natural language understanding and generation. Notably, the output control and alignment with the input of LLMs can be refined through instruction tuning.…
Large language models (LLMs) with Chain-of-Thought (CoT) reasoning have achieved strong performance across diverse tasks, including mathematics, coding, and general reasoning. A distinctive ability of these reasoning models is…
Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or…
Reinforcement learning-based retrieval-augmented generation (RAG) methods enhance the reasoning abilities of large language models (LLMs). However, most rely only on final-answer rewards, overlooking intermediate reasoning quality. This…
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
The constitutional framework of alignment aims to align large language models (LLMs) with value-laden principles written in natural language (such as to avoid using biased language). Prior work has focused on parameter fine-tuning…
Reinforcement learning (RL) training of large language models (LLMs) on unverifiable tasks is challenging even when a reasonable-quality reference answer is available. We propose a constrained RL training framework that (i) optimizes a…
Objectives: Large language models (LLMs) can harness medical knowledge for intelligent question answering (Q&A), promising support for auxiliary diagnosis and medical talent cultivation. However, there is a deficiency of highly efficient…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
The Refinement Calculus of Reactive Systems (RCRS) is a compositional formal framework for modeling and reasoning about reactive systems. RCRS provides a language which allows to describe atomic components as symbolic transition systems or…
Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models…
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…