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Since their recent introduction, process trees have been frequently used as a process modeling formalism in many process mining algorithms. A process tree is a tree-based model of a process, in which internal vertices represent behavioral…
There is no known way of giving a domain-theoretic semantics to higher-order probabilistic languages, in such a way that the involved domains are continuous or quasi-continuous - the latter is required to do any serious mathematics. We…
Large Language Models (LLMs) excel at understanding natural language but struggle with explicit commonsense reasoning. A recent trend of research suggests that the combination of LLM with robust symbolic reasoning systems can overcome this…
In standard process algebra, parallel components do not share a common state and communicate through synchronisation. The advantage of this type of communication is that it facilitates compositional reasoning. For modelling and analysing…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…
Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning…
Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
The predominant challenge in weakly supervised semantic parsing is that of spurious programs that evaluate to correct answers for the wrong reasons. Prior work uses elaborate search strategies to mitigate the prevalence of spurious…
We present the formalism of sequential and asynchronous processes defined in terms of random or quantum grammars and argue that these processes have relevance in genomics. To make the article accessible to the non-mathematicians, we keep…
Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. In the past, two independent hierarchies have been obtained for external and internal…
We consider the problem of estimating the context tree of a stationary ergodic process with finite alphabet without imposing additional conditions on the process. As a starting point we introduce a Hamming metric in the space of irreducible…
We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting…
We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to…
Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical…
Multi-step reasoning instruction, such as chain-of-thought prompting, is widely adopted to explore better language models (LMs) performance. We report on the systematic strategy that LMs employ in such a multi-step reasoning process. Our…
The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are…
Generative Artificial Intelligence (AI) has rapidly become a powerful tool, capable of generating various types of data, such as images and text. However, despite the significant advancement of generative AI, time series generative AI…