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Large Language Models (LLMs) are often described as instances of foundation models that possess strong generalization obeying scaling laws, and therefore transfer robustly across various conditions in few- or zero-shot manner. Such claims…
This paper explores how natural-language descriptions of formal languages can be compared to their formal representations and how semantic differences can be explained. This is motivated from educational scenarios where learners describe a…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
This paper presents a comprehensive examination of the impact of tokenization strategies and vocabulary sizes on the performance of Arabic language models in downstream natural language processing tasks. Our investigation focused on the…
Recent advancements in Large Language Models (LLMs) harness linguistic associations in vast natural language data for practical applications. However, their ability to understand the physical world using only language data remains a…
In this paper we develop a formal system called Natural Term Logic (NTL). NTL aims to represent key aspects of the logical and grammatical mechanisms of natural language as well as grammatical transformations which preserve core logical…
In the medical domain, the continuous stream of scientific research contains contradictory results supported by arguments and counter-arguments. As medical expertise occurs at different levels, part of the human agents have difficulties to…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the…
Compact closed categories have found applications in modeling quantum information protocols by Abramsky-Coecke. They also provide semantics for Lambek's pregroup algebras, applied to formalizing the grammatical structure of natural…
High-quality WordNets are crucial for achieving high-quality results in NLP applications that rely on such resources. However, the wordnets of most languages suffer from serious issues of correctness and completeness with respect to the…
The tractability conjecture for finite domain Constraint Satisfaction Problems (CSPs) stated that such CSPs are solvable in polynomial time whenever there is no natural reduction, in some precise technical sense, from the 3-SAT problem;…
In R.D. Sorkin's framework for logic in physics a clear separation is made between the collection of unasserted propositions about the physical world and the affirmation or denial of these propositions by the physical world. The unasserted…
Design methods in information systems frequently create software descriptions using formal languages. Nonetheless, most software designers prefer to describe software using natural languages. This distinction is not simply a matter of…
Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…
Large language models (LLMs) reason over discrete token ID sequences, yet modern subword tokenizers routinely produce non-unique encodings: multiple token ID sequences can detokenize to identical surface strings. This representational…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
This work investigates how effectively large language models (LLMs) and their tokenization schemes represent and generate Arabic root-pattern morphology, probing whether they capture genuine morphological structure or rely on surface…