Related papers: A Modular Lean 4 Framework for Confluence and Stro…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
Recent large language models (LLMs) perform strongly on mathematical benchmarks yet often misapply lemmas, importing conclusions without validating assumptions. We formalize lemma$-$judging as a structured prediction task: given a statement…
In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound variables and meta-variables. Its typing discipline is derived from contextual modal type theory. We first present a dependently typed…
De Bruijn and Newman introduced a deformation of the completed Riemann zeta function $\zeta$, and proved there is a real constant $\Lambda$ which encodes the movement of the nontrivial zeros of $\zeta$ under the deformation. The Riemann…
In this paper, we take a pervasively effectful (in the style of ML) typed lambda calculus, and show how to extend it to permit capturing pure expressions with types. Our key observation is that, just as the pure simply-typed lambda calculus…
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
We introduce the G\"odel Mirror, a formal system defined in Lean 4 that treats contradiction as a control signal for recursive structural evolution. Inspired by G\"odelian self-reference, our system's operational semantics encode symbolic…
The refinement calculus provides a methodology for transforming an abstract specification into a concrete implementation, by following a succession of refinement rules. These rules have been mechanized in theorem-provers, thus providing a…
Recent advances in product bundling have leveraged multimodal information through sophisticated encoders, but remain constrained by limited semantic understanding and a narrow scope of knowledge. Therefore, some attempts employ In-context…
To achieve generalized and robust natural-to-formal language conversion (N2F), large language models (LLMs) need to have strong capabilities of decomposition and composition in N2F when faced with an unfamiliar formal language and be able…
Recently, large language models have presented promising results in aiding formal mathematical reasoning. However, their performance is restricted due to the scarcity of formal theorem-proving data, which requires additional effort to be…
We study a unified framework for optimization problems defined on dual-modular instances, where the input comprises a finite ground set $V$ and two set functions: a monotone supermodular reward function $\f$ and a strictly monotone…
Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…
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…
Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to…
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda…
Modern neural network architectures still struggle to learn algorithmic procedures that require to systematically apply compositional rules to solve out-of-distribution problem instances. In this work, we focus on formula simplification…
Confluence of a nondeterministic program ensures a functional input-output relation, freeing the programmer from considering the actual scheduling strategy, and allowing optimized and perhaps parallel implementations. The more general…
We present a new, uniform semantics for Haskell-style overloading. We realize our approach in a new core language, System F$_\mathrm{D}$, whose metatheory we mechanize in the Lean4 interactive theorem prover. System F$_\mathrm{D}$ is…