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Oz is a multiparadigm language that supports logic programming as one of its major paradigms. A multiparadigm language is designed to support different programming paradigms (logic, functional, constraint, object-oriented, sequential,…
Formal specifications, such as pre- and post-conditions provide a solid basis for performing thorough program verification. However, developers rarely provide such formal specifications, hence if AI could help in constructing them, it would…
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout…
The massive progress of machine learning has seen its application over a variety of domains in the past decade. But how do we develop a systematic, scalable and modular strategy to validate machine-learning systems? We present, to the best…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
Large language models (LLMs) have demonstrated potential in reasoning tasks, but their performance on linguistics puzzles remains consistently poor. These puzzles, often derived from Linguistics Olympiad (LO) contests, provide a minimal…
In the last decade, a large body of work has emerged on robustness of neural networks, i.e., checking if the decision remains unchanged when the input is slightly perturbed. However, most of these approaches ignore the confidence of a…
Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…
In this paper we give instructions on how to write a minimalist grammar (MG). In order to present the instructions as an algorithm, we use a variant of context free grammars (CFG) as an input format. We can exclude overgeneration, if the…
Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…
Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that…
This research introduces a new parsing approach, based on earlier syntactic work on context free grammar (CFG) and generalized phrase structure grammar (GPSG). The approach comprises both a new parsing algorithm and a set of syntactic rules…
A core component of a successful artificial general intelligence would be the rapid creation and manipulation of grounded compositional abstractions and the demonstration of expertise in the family of recursive hierarchical syntactic…
The performance of large language models (LLMs) has recently improved to the point where models can perform well on many language tasks. We show here that--for the first time--the models can also generate valid metalinguistic analyses of…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
We study the membership problem to context-free languages L (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters (assuming independence across positions). Our task is to compute, given a…
The Object Constraint Language (OCL) is a declarative language that adds constraints and object query expressions to MOF models. Despite its potential to provide precision and conciseness to UML models, the unfamiliar syntax of OCL has…
Recent advancements in large language models (LLMs) have led to significant breakthroughs in mathematical reasoning capabilities. However, existing benchmarks like GSM8K or MATH are now being solved with high accuracy (e.g., OpenAI o1…
In task-oriented conversation systems, natural language generation systems that generate sentences with specific information related to conversation flow are useful. Our study focuses on language generation by considering various…
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…