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Recent work in machine learning increasingly attributes human-like capabilities such as reasoning or theory of mind to large language models (LLMs) on the basis of benchmark performance. This paper examines this practice through the lens of…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
Numbers are a basic part of how humans represent and describe the world around them. As a consequence, learning effective representations of numbers is critical for the success of large language models as they become more integrated into…
Large language models (LLMs) have emerged as powerful tools for many AI problems and exhibit remarkable in-context learning (ICL) capabilities. Compositional ability, solving unseen complex tasks that combine two or more simple tasks, is an…
Ontologies are useful for automatic machine processing of domain knowledge as they represent it in a structured format. Yet, constructing ontologies requires substantial manual effort. To automate part of this process, large language models…
It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities…
Out-of-distribution generalization capabilities of sequence-to-sequence models can be studied from the lens of two crucial forms of generalization: length generalization -- the ability to generalize to longer sequences than ones seen during…
Requirements classification assigns natural language requirements to predefined classes, such as functional and non functional. Accurate classification reduces risk and improves software quality. Most existing models rely on supervised…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
Despite their outstanding performance, large language models (LLMs) suffer notorious flaws related to their preference for simple, surface-level textual relations over full semantic complexity of the problem. This proposal investigates a…
The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such…
Similarly to the Chomsky hierarchy, we offer a classification of communication complexity measures such that these measures are organized into equivalence classes. Different from previous attempts of this endeavor, we consider two…
Counting the number of models of a Boolean formula is a fundamental problem in artificial intelligence and reasoning. Minimal models of a Boolean formula are critical in various reasoning systems, making the counting of minimal models…
A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
Attributing outputs from Large Language Models (LLMs) in adversarial settings-such as cyberattacks and disinformation campaigns-presents significant challenges that are likely to grow in importance. We approach this attribution problem from…
We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several…
Large Language Models (LLMs) are increasingly described as possessing strong reasoning capabilities, supported by high performance on mathematical, logical, and planning benchmarks. However, most existing evaluations rely on aggregate…