Related papers: Sentence complexity of theorems in Mizar
The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on…
Progress in sentence simplification has been hindered by a lack of labeled parallel simplification data, particularly in languages other than English. We introduce MUSS, a Multilingual Unsupervised Sentence Simplification system that does…
Every countable structure has a sentence of the infinitary logic $\mathcal{L}_{\omega_1 \omega}$ which characterizes that structure up to isomorphism among countable structures. Such a sentence is called a Scott sentence, and can be thought…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
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…
Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilized in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
If a concept is not well defined, there are grounds for its abuse. This is particularly true of complexity, an inherently interdisciplinary concept that has penetrated very different fields of intellectual activity from physics to…
We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…
Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling…
Machine learning is a thriving part of computer science. There are many efficient approaches to machine learning that do not provide strong theoretical guarantees, and a beautiful general learning theory. Unfortunately, machine learning…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…