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To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of…

When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters' values is a popular and effective approach. Decision-focused learning (DFL) aims at learning a…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

This paper defines the (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern SAT-solvers. The resolution inference is restricted to (first-order) unit-propagation and the…

We consider variations on the following problem: given an NFA M and a pattern p, does there exist an x in L(M) such that p matches x? We consider the restricted problem where M only accepts a finite language. We also consider the variation…

This work proposes a simple training-free prompt-free approach to leverage large language models (LLMs) for the Chinese spelling correction (CSC) task, which is totally different from all previous CSC approaches. The key idea is to use an…

Morphological declension, which aims to inflect nouns to indicate number, case and gender, is an important task in natural language processing (NLP). This research proposal seeks to address the degree to which Recurrent Neural Networks…

We propose a general method to break down a main complex task into a set of intermediary easier sub-tasks, which are formulated in natural language as binary questions related to the final target task. Our method allows for representing…

Neural network models have been demonstrated to be capable of achieving remarkable performance in sentence and document modeling. Convolutional neural network (CNN) and recurrent neural network (RNN) are two mainstream architectures for…

Decision-Focused Learning (DFL) is an emerging learning paradigm that tackles the task of training a machine learning (ML) model to predict missing parameters of an incomplete optimization problem, where the missing parameters are…

Model generalization ability upon incrementally acquiring dynamically updating knowledge from sequentially arriving tasks is crucial to tackle the sensitivity-stability dilemma in Continual Learning (CL). Weight loss landscape sharpness…

We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…

One of the long-standing goals in optimisation and constraint programming is to describe a problem in natural language and automatically obtain an executable, efficient model. Large language models appear to bring this vision closer,…

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…

The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Generalizing a previous result, we produce a new family of regular languages on a two-letter alphabet having arbitrary high…

Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an…

We present a novel and well automatable approach to formal verification of programs with underspecified semantics, i.e., a language semantics that leaves open the order of certain evaluations. First, we reduce this problem to…

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential…

Neural collapse ($\mathcal{NC}$) is a phenomenon observed in classification tasks where top-layer representations collapse into their class means, which become equinorm, equiangular and aligned with the classifiers. These behaviours --…

Attention, specifically scaled dot-product attention, has proven effective for natural language, but it does not have a mechanism for handling hierarchical patterns of arbitrary nesting depth, which limits its ability to recognize certain…