Related papers: Inductive Reasoning for Coinductive Types

We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its…

Chain-of-Thought reasoning can enhance large language models, but it requires manually designed prompts to guide the model. Recently proposed CoT-decoding enables the model to generate CoT-style reasoning paths without prompts, but it is…

The Aldous diffusion is a conjectured Markov process on the space of real trees that is the continuum analogue of discrete Markov chains on binary trees. We construct this conjectured process via a consistent system of stationary evolutions…

An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…

Quotient inductive-inductive types (QIITs) are generalized inductive types which allow sorts to be indexed over previously declared sorts, and allow usage of equality constructors. QIITs are especially useful for algebraic descriptions of…

Training Large Language Models (LLMs) for chain-of-thought reasoning presents a significant challenge: supervised fine-tuning on a single "golden" rationale hurts generalization as it penalizes equally valid alternatives, whereas…

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…

We propose a novel approach for answering and explaining multiple-choice science questions by reasoning on grounding and abstract inference chains. This paper frames question answering as an abductive reasoning problem, constructing…

We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…

Modern language models address complex questions through chain-of-thought (CoT) reasoning (Wei et al., 2023) and retrieval augmentation (Lewis et al., 2021), yet struggle with error propagation and knowledge integration. Tree-structured…

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…

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want…

In this paper, I establish the categorical structure necessary to interpret dependent inductive and coinductive types. It is well-known that dependent type theories \`a la Martin-L\"of can be interpreted using fibrations. Modern theorem…

We combine the theory of inductive data types with the theory of universal measurings. By doing so, we find that many categories of algebras of endofunctors are actually enriched in the corresponding category of coalgebras of the same…

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…

Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be…

Despite the progress of foundation models, knowledge-based reasoning remains a persistent challenge due to their limited capacity for knowledge recall and inference. Existing methods primarily focus on encouraging these models to plan and…

Chain-of-Thought (CoT) is a critical technique in enhancing the reasoning ability of Large Language Models (LLMs), and latent reasoning methods have been proposed to accelerate the inefficient token-level reasoning chain. We notice that…

Bayesian belief networks can be used to represent and to reason about complex systems with uncertain, incomplete and conflicting information. Belief networks are graphs encoding and quantifying probabilistic dependence and conditional…

This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…