Related papers: Pumping Lemma for Higher-order Languages
OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language.…
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is…
Sentiment-aware intelligent systems are essential to a wide array of applications. These systems are driven by language models which broadly fall into two paradigms: Lexicon-based and contextual. Although recent contextual models are…
We study the task, for a given language $L$, of enumerating the (generally infinite) sequence of its words, without repetitions, while bounding the delay between two consecutive words. To allow for delay bounds that do not depend on the…
Language models have become the backbone of today's AI systems. However, their predominant left-to-right generation limits the use of bidirectional context, which is essential for tasks that involve filling text in the middle. We propose…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
Large language models (LLMs) have accomplished remarkable reasoning performance in various domains. However, in the domain of reasoning tasks, we discover a frailty: LLMs are surprisingly brittle to the ordering of the premises, despite the…
We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include…
Latent tree learning(LTL) methods learn to parse sentences using only indirect supervision from a downstream task. Recent advances in latent tree learning have made it possible to recover moderately high quality tree structures by training…
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
We consider the problem of computing the measure of a regular set of infinite binary trees. While the general case remains unsolved, we show that the measure of a language can be computed when the set is given in one of the following three…
We consider languages defined by signed grammars which are similar to context-free grammars except productions with signs associated to them are allowed. As a consequence, the words generated also have signs. We use the structure of the…
We use reinforcement learning to learn tree-structured neural networks for computing representations of natural language sentences. In contrast with prior work on tree-structured models in which the trees are either provided as input or…
Large language models (LLMs) perform well at a myriad of tasks, but explaining the processes behind this performance is a challenge. This paper investigates whether LLMs can give faithful high-level explanations of their own internal…
This paper investigates the reliability of explanations generated by large language models (LLMs) when prompted to explain their previous output. We evaluate two kinds of such self-explanations - extractive and counterfactual - using three…
In derivational morphology, what mechanisms govern the variation in form-meaning relations between words? The answers to this type of questions are typically based on intuition and on observations drawn from limited data, even when a wide…
We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Recent large language models (LLMs) perform strongly on mathematical benchmarks yet often misapply lemmas, importing conclusions without validating assumptions. We formalize lemma$-$judging as a structured prediction task: given a statement…
Indexed languages are interesting in computational linguistics because they are the least class of languages in the Chomsky hierarchy that has not been shown not to be adequate to describe the string set of natural language sentences. We…