相关论文: Cut-free LK quasi-polynomially simulates resolutio…

Inspired by the recent evolution of deep neural networks (DNNs) in machine learning, we explore their application to PL-related topics. This paper is the first step towards this goal; we propose a proof-synthesis method for the…

The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called "Lambek's restriction," that is, the antecedent of any provable…

Scalable oversight protocols aim to enable humans to accurately supervise superhuman AI. In this paper we study debate, where two AI's compete to convince a judge; consultancy, where a single AI tries to convince a judge that asks…

Knowledge compilation studies the trade-off between succinctness and efficiency of different representation languages. For many languages, there are known strong lower bounds on the representation size, but recent work shows that, for some…

As reasoning LLMs increasingly trade tokens for accuracy through deliberation, search, and self-correction, a single accuracy score can no longer tell whether those tokens buy useful reasoning, recovery from hard instances, or unnecessary…

We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…

We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…

We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity,…

This article is about both approximation theory and the numerical solution of partial differential equations (PDEs). First we introduce the notion of {\em reciprocal-log} or {\em log-lightning approximation} of analytic functions with…

Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the…

Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the…

We show that for Multiplicative Exponential Linear Logic (without weakenings) the syntactical equivalence relation on proofs induced by cut-elimination coincides with the semantic equivalence relation on proofs induced by the multiset based…

I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction…

Large language models (LLMs) have exhibited impressive capabilities across a myriad of tasks, yet they occasionally yield undesirable outputs. We posit that these limitations are rooted in the foundational autoregressive architecture of…

This work explores the role of prompt design and judge selection in LLM-as-a-Judge evaluations of free text legal question answering. We examine whether automatic task prompt optimization improves over human-centered design, whether…

In this paper, we study proof systems in the sense of Cook-Reckhow for problems that are higher in the polynomial hierarchy than coNP, in particular, #SAT and maxSAT. We start by explaining how the notion of Cook-Reckhow proof systems can…

A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…

Large language models (LLMs) have become indispensable, but the most celebrated efficiency methods -- mixture-of-experts (MoE), speculative decoding, and complex retrieval-augmented generation (RAG) -- were built for hyperscale providers…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

Recently, structure learning of directed acyclic graphs (DAGs) has been formulated as a continuous optimization problem by leveraging an algebraic characterization of acyclicity. The constrained problem is solved using the augmented…