Related papers: Logic Characterization of Floyd Languages
Whereas the semantics of probabilistic languages has been extensively studied, specification languages for their properties have received less attention -- with the notable exception of recent and on-going efforts by Joost-Pieter Katoen and…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main…
Families of DFAs (FDFAs) have recently been introduced as a new representation of $\omega$-regular languages. They target ultimately periodic words, with acceptors revolving around accepting some representation $u\cdot v^\omega$. Three…
Large Language Models (LLMs) have emerged as dominant foundational models in modern NLP. However, the understanding of their prediction processes and internal mechanisms, such as feed-forward networks (FFN) and multi-head self-attention…
A logic formalism is presented which increases the expressive power of the ID/LP format of GPSG by enlarging the inventory of ordering relations and extending the domain of their application to non-siblings. This allows a concise, modular…
Large pre-trained language models such as BERT have been widely used as a framework for natural language understanding (NLU) tasks. However, recent findings have revealed that pre-trained language models are insensitive to word order. The…
The confluence of Federated Learning (FL) and Large Language Models (LLMs) is ushering in a new era in privacy-preserving natural language processing. However, the intensive memory requirements for fine-tuning LLMs pose significant…
Permutations can be viewed as pairs of linear orders, or more formally as models over a signature consisting of two binary relation symbols. This approach was adopted by Albert, Bouvel and F\'eray, who studied the expressibility of…
Action description languages, such as A and B, are expressive instruments introduced for formalizing planning domains and planning problem instances. The paper starts by proposing a methodology to encode an action language (with conditional…
This paper establishes model-theoretic properties of $\mathrm{FOE}^{\infty}$, a variation of monadic first-order logic that features the generalised quantifier $\exists^\infty$ (`there are infinitely many'). We provide syntactically defined…
Automata operating on pairs of words were introduced as an alternative way of capturing acceptance of regular $\omega$-languages. Families of DFAs and lasso automata operating on such pairs followed, giving rise to minimisation algorithms,…
Since the advent of Federated Learning (FL), research has applied these methods to natural language processing (NLP) tasks. Despite a plethora of papers in FL for NLP, no previous works have studied how multilingual text impacts FL…
To expand a fundamental theory of context-free languages, we equip nondeterministic one-way pushdown automata with additional oracle mechanisms, which naturally induce various nondeterministic reducibilities among formal languages. As a…
We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three…
Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…
Teaching logic effectively requires an understanding of the factors which cause logic students to struggle. Formalization exercises, which require the student to produce a formula corresponding to the natural language sentence, are a good…
Arguably, omega-regular languages play an important role as a specification formalism in many approaches to systems monitoring via runtime verification. However, since their elements are infinite words, not every omega-regular language can…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…