Related papers: Formal semantics of language and the Richard-Berry…
It is customary to expect from a logical system that it can be algebraizable, in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa's paraconsistent calculi $C_n$, algebraic…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata)…
Human languages employ constructions that tacitly assume specific properties of the limited range of phenomena they evolved to describe. These assumed properties are true features of that limited context, but may not be general or precise…
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…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
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…
LLMorphism is the biased belief that human cognition works like a large language model. I argue that the rise of conversational LLMs may make this bias increasingly psychologically available. When artificial systems produce human-like…
Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and…
Formal Semantics and Distributional Semantics are two important semantic frameworks in Natural Language Processing (NLP). Cognitive Semantics belongs to the movement of Cognitive Linguistics, which is based on contemporary cognitive…
Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…
Foundations of formal languages, as subfield of theoretical computer science, are part of typical upper secondary education curricula. There is very little research on the potential difficulties that students at this level have with this…
Counterfactuals have become an important area of interdisciplinary interest, especially in logic, philosophy of language, epistemology, metaphysics, psychology, decision theory, and even artificial intelligence. In this study, we propose a…
Natural language numbers are an example of compositional structures, where larger numbers are composed of operations on smaller numbers. Given that compositional reasoning is a key to natural language understanding, we propose novel…
We describe two systems currently being developed that use large language models for the automatized correction of (i) exercises in translating back and forth between natural language and the languages of propositional logic and first-order…
Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…