The Nature and Future of Axiomatic Systems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Hilbert’s Sixth Problem".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 335

Special Issue Editors


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Guest Editor
Associate Professor of Mathematics, Connectivity Program, Faculty of International Liberal Arts Global, Akita International University, Akita, Japan
Interests: computational semigroup theory; algebraic biology; theory of computation; evolutionary computation
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Guest Editor
Institute of Mathematics and Computer Science, Eszterhazy Karoly University, 3300 Eger, Hungary
Interests: geometry; computer graphics; philosophy of science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The ideal form of the description of mathematical knowledge is generally thought to be the axiomatic approach: the laws of logical inference and a few statements define a mathematical topic.

As the ultimate form of compression, this approach realizes mathematics' efficient elegance and unity. However, there are issues. First, it may be challenging to decompress: finding whether a statement is a logical consequence of the axioms takes work. This endeavor is the realm of automated theorem proving. How to find solid proof by computers is a topic of ongoing research. Moreover, as we have learned in the development of mathematical logic, it could be impossible in some instances. These are the philosophical limits of mathematics, and the ramifications still need to be fully understood.

A recent issue is the involvement of AI-based frameworks (such as Large Language Models) in mathematical discovery and description. Can and will these frameworks follow the axiomatic pathway? We also need to consider the perspective of education. Is the axiomatic treatment the most conducive to understanding? Or, as it may feel to the learner, why do we have islands of concepts connected in tangled webwork but not crystallized from a tiny seed? If understanding does not require solid foundations, is the axiomatic approach simply a historical tradition? 

For this Special Issue, we invite both types of contributions: those that are `inside', e.g., theorem-proving, axiomatic treatment of a mathematical topic; and those from 'outside', e.g., critical philosophical work and papers investigating the educational aspects of axiomatic systems. 

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

  • Theorem proving;
  • Axiomatic treatment of a mathematical topic;
  • Axiomatism and artificial intelligence;
  • Educational aspects of axiomatic systems. 

We look forward to receiving your contributions.

Dr. Attila Egri-Nagy
Prof. Dr. Miklos Hoffmann
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • axiomatic systems
  • theorem proving
  • artificial intelligence
  • mathematical logic
  • mathematics education

Published Papers

This special issue is now open for submission.
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