Related papers: From Double Pushout Grammars to Hypergraph Lambek …

Direct Preference Optimization (DPO) has become a prominent method for aligning Large Language Models (LLMs) with human preferences. While DPO has enabled significant progress in aligning English LLMs, multilingual preference alignment is…

In functional programming, point-free relation calculi have been fruitful for general theories of program construction, but for specific applications pointwise expressions can be more convenient and comprehensible. In imperative…

This paper generalizes the encoding of argumentation frameworks beyond the classical 2-valued propositional logic system ($PL_2$) to 3-valued propositional logic systems ($PL_3$s) and fuzzy propositional logic systems ($PL_{[0,1]}s$),…

We investigate the building of unified models that can predict the matter-density power spectrum and the two-point correlation function from very large to small scales, being consistent with perturbation theory at low $k$ and with halo…

The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…

Large Language Models (LLMs) have demonstrated remarkable proficiency in English mathematical reasoning, yet a significant performance disparity persists in multilingual contexts, largely attributed to deficiencies in language…

Usually, a parser for an $LR(k)$-grammar $G$ is a deterministic pushdown transducer which produces backwards the unique rightmost derivation for a given input string $x \in L(G)$. The best known upper bound for the size of such a parser is…

Diffusion language models (DLMs) enable parallel, order-agnostic generation with iterative refinement, offering a flexible alternative to autoregressive large language models (LLMs). However, adapting reinforcement learning (RL) fine-tuning…

We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus (specifically: every analytic structural rule…

Direct Preference Optimization (DPO) is an effective framework for aligning large language models with human preferences, but it struggles with complex reasoning tasks. DPO optimizes for the likelihood of generating preferred over…

In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should…

Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…

We introduce a proof system for Hajek's logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL, are sound and invertible with respect to any valuation of BL into a suitable…

We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill's calculi, and focus on their fragments…

We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok-Esakia…

We find a generalization of the restricted PBW basis for pointed Hopf algebras over abelian groups constructed by Kharchenko. We obtain a factorization of the Hilbert series for a wide class of graded Hopf algebras. These factors are…

Current directed graph embedding methods build upon undirected techniques but often inadequately capture directed edge information, leading to challenges such as: (1) Suboptimal representations for nodes with low in/out-degrees, due to the…

The technique of \emph{equality saturation}, which equips graphs with an equivalence relation, has proven effective for program optimisation. We give a categorical semantics to these structures, called \emph{e-graphs}, in terms of Cartesian…

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path…

Direct Preference Optimization (DPO) has emerged as a prominent algorithm for the direct and robust alignment of Large Language Models (LLMs) with human preferences, offering a more straightforward alternative to the complex Reinforcement…