Related papers: Superposition as a logical glue
Reasoning about tabular information presents unique challenges to modern NLP approaches which largely rely on pre-trained contextualized embeddings of text. In this paper, we study these challenges through the problem of tabular natural…
Mathematical documents written in LaTeX often contain ambiguities. We can resolve some of them via semantic markup using, e.g., sTeX, which also has other potential benefits, such as interoperability with computer algebra systems, proof…
Despite the successes of large language models (LLMs), they exhibit significant drawbacks, particularly when processing long contexts. Their inference cost scales quadratically with respect to sequence length, making it expensive for…
This article introduces the conjecture that "mathematics, logic and related disciplines may usefully be understood as information compression (IC) by 'multiple alignment', 'unification' and 'search' (ICMAUS)". As a preparation for the two…
Logic is a foundation for many modern areas of computer science. In artificial intelligence, as a basis of database query languages, as well as in formal software and hardware verification --- modelling scenarios using logical formalisms…
In natural language, words and phrases themselves imply the semantics. In contrast, the meaning of identifiers in mathematical formulae is undefined. Thus scientists must study the context to decode the meaning. The Mathematical Language…
We extend classical Propositional Logic (PL) by adding a new primitive binary connective $\varphi|\psi$, intended to represent the "superposition" of sentences $\varphi$ and $\psi$, an operation motivated by the corresponding notion of…
Model merging, such as model souping, is the practice of combining different models with the same architecture together without further training. In this work, we present a model merging methodology that addresses the difficulty of…
In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…
Why should computers interpret language incrementally? In recent years psycholinguistic evidence for incremental interpretation has become more and more compelling, suggesting that humans perform semantic interpretation before constituent…
Existing approaches to mathematical reasoning with large language models (LLMs) rely on Chain-of-Thought (CoT) for generalizability or Tool-Integrated Reasoning (TIR) for precise computation. While efforts have been made to combine these…
Idiomatic expressions are an integral part of natural language and constantly being added to a language. Owing to their non-compositionality and their ability to take on a figurative or literal meaning depending on the sentential context,…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could…
In order to effectively manage the overwhelming influx of data, it is crucial to ensure that data is findable, accessible, interoperable, and reusable (FAIR). While ontologies and knowledge graphs have been employed to enhance FAIRness,…
Information Integration is a young and exciting field with enormous research and commercial significance in the new world of the Information Society. It stands at the crossroad of Databases and Artificial Intelligence requiring novel…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…