Related papers: INDUCTION: Finite-Structure Concept Synthesis in F…
Language generation maps a rich, high-dimensional internal state to a single token sequence. We study this many-to-one mapping through the lens of intention collapse: the projection from an internal intention space I to an external language…
First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…
We introduce STREET, a unified multi-task and multi-domain natural language reasoning and explanation benchmark. Unlike most existing question-answering (QA) datasets, we expect models to not only answer questions, but also produce…
In the logical framework introduced by Grohe and Tur\'an (TOCS 2004) for Boolean classification problems, the instances to classify are tuples from a logical structure, and Boolean classifiers are described by parametric models based on…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
We introduce seqBench, a parametrized benchmark for probing sequential reasoning limits in Large Language Models (LLMs) through precise, multi-dimensional control over several key complexity dimensions. seqBench allows systematic variation…
Large language models perform well on many logical reasoning benchmarks, but it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a benchmark that isolates three fundamental logical…
Methods based on representation learning currently hold the state-of-the-art in many natural language processing and knowledge base inference tasks. Yet, a major challenge is how to efficiently incorporate commonsense knowledge into such…
The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on…
We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…
The tremendous expanse of search engines, dictionary and thesaurus storage, and other text mining applications, combined with the popularity of readily available scanning devices and optical character recognition tools, has necessitated…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…
We propose SETI (Systematicity Evaluation of Textual Inference), a novel and comprehensive benchmark designed for evaluating pre-trained language models (PLMs) for their systematicity capabilities in the domain of textual inference.…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
In generative commonsense reasoning tasks such as CommonGen, generative large language models (LLMs) compose sentences that include all given concepts. However, when focusing on instruction-following capabilities, if a prompt specifies a…