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Axioms
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15th Anniversary of Axioms: Logic
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15th Anniversary of Axioms: Logic

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1785

Editor

Prof. Dr. Darjan Karabašević

E-Mail Website
Guest Editor
1. Faculty of Applied Management, Economics and Finance in Belgrade, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia
2. College of Global Business, Korea University, Sejong 30019, Republic of Korea
Interests: multiple-criteria decision-making (MCDM); decision support systems (DSSs); computational intelligence; decision-making theory; informatics; management
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Considering that Axioms is celebrating its 15th anniversary, we are pleased to announce a Special Issue in the Logic section that is dedicated to attracting high-quality papers related to recent advances and future directions of mathematical logic, together with multiple-criteria decision-making (MCDM) and computational intelligence (CI).

Mathematical logic, as an important field of mathematics, together with multiple-criteria decision-making (MCDM) and computational intelligence (CI), has a fundamental role in addressing complex decision problems that are characterized by uncertainty, ambiguity, and dynamic environments. This Special Issue will consider high-quality papers in the field of logic, mathematical logic, and their application, with a particular emphasis on computability, fuzzy logic, algorithmic and combinatorial optimization, logic-based intelligent decision-making, innovative MCDM methodologies, hybrid models and integrated approaches, and real-world applications.

We invite scholars to contribute their latest findings and join us in celebrating the continued growth and the impact of the Axioms journal. Therefore, topics include, but are not limited to, the following:

  • Mathematical logic and its applications;
  • Fuzzy systems and fuzzy logic;
  • Computability and recursion theory;
  • Algorithmic and combinatorial optimization;
  • Decision theory and methods;
  • Multiple-criteria decision-making;
  • Decision support systems;
  • Fuzzy, neutrosophic, and grey MCDM methods;
  • Computational intelligence (neural networks, evolutionary algorithms, and swarm intelligence);
  • Probabilistic methods.

Prof. Dr. Darjan Karabašević
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • mathematical logic
  • fuzzy systems and fuzzy logic
  • computability and recursion theory
  • multiple-criteria decision-making
  • computational intelligence

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

34 pages, 1025 KB  
Article
Approximating Heterotypic Bisimulations for Weighted Finite Automata over the Field of Real Numbers
by Predrag Stanimirović, Miroslav Ćirić, Darjan Karabašević and Dimitrios Gerontitis
Axioms 2026, 15(8), 555; https://doi.org/10.3390/axioms15080555 - 23 Jul 2026
Viewed by 360
Abstract
This paper examines the existence and approximation of bisimulations between weighted finite automata (WFAs) over the real numbers. It shows that forward–backward bisimulation (fbb) and backward–forward bisimulation (bfb) between two WFAs are equivalent to solving specific homogeneous Sylvester equations and two vector equations. [...] Read more.
This paper examines the existence and approximation of bisimulations between weighted finite automata (WFAs) over the real numbers. It shows that forward–backward bisimulation (fbb) and backward–forward bisimulation (bfb) between two WFAs are equivalent to solving specific homogeneous Sylvester equations and two vector equations. The transition matrices of the automata serve as the coefficient matrices in these equations. This approach reformulates the WFA’s problem as a linear algebra task involving real coefficient matrices. Obtained systems of vector and matrix equations frequently lack consistency. Multi-criteria optimization can address these inconsistencies. We apply continuous-time zeroing neural network (ZNN) dynamics to find approximate solutions for these inconsistent vector-matrix systems. Since ZNN dynamics are globally convergent, they generate approximate solutions that evolve over time. Simulation experiments are conducted on random transition matrices, using various initial state matrices and two activation functions. Full article
(This article belongs to the Special Issue 15th Anniversary of Axioms: Logic)
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49 pages, 632 KB  
Article
EPiC: A Four-Valued Evidential Constraint Calculus for First-Order Reasoning
by José Oscar Olmedo-Aguirre, Isaac Machorro-Cano, Giner Alor-Hernández, Lisbeth Rodríguez-Mazahua, José Luis Sánchez-Cervantes and Aura Lucina Kantún-Montiel
Axioms 2026, 15(7), 508; https://doi.org/10.3390/axioms15070508 - 6 Jul 2026
Viewed by 632
Abstract
This article introduces the Evidence Propagation Calculus (EPiC), an operational framework for first-order reasoning built on a simple but productive observation: familiar inference patterns such as Modus Ponens and Modus Tollens behave like the movement of evidential markers across a structured graph. Positive [...] Read more.
This article introduces the Evidence Propagation Calculus (EPiC), an operational framework for first-order reasoning built on a simple but productive observation: familiar inference patterns such as Modus Ponens and Modus Tollens behave like the movement of evidential markers across a structured graph. Positive evidence at an antecedent propagates forward to the consequent; negative evidence at a consequent propagates backward. When both markers coexist at a node, the system is locally inconsistent but not operationally broken. To make this observation precise, EPiC grounds reasoning in a four-valued evidential domain V={N,T,F,B}, where N denotes absence of evidence, T positive evidence, F negative evidence, and B their coexistence. Each logical connective is assigned a local evidential table, and inference is treated uniformly as the progressive restriction of admissible configurations under an evidential order: inadmissible values are eliminated, minimal surviving values are selected as the next effective evidential states, and the resulting restrictions propagate across shared variables. Compound formulas are decomposed into families of local unary and binary constraints through auxiliary variables, making the propagation process explicit and structurally uniform. Within this setting, Modus Ponens, Modus Tollens, and polarity-switching negation are not postulated as primitive rules. They emerge as derived consequences of the same local table calculus. The framework distinguishes different operational routes of justification. In some cases, positive support reaches the target formula directly through successive local restrictions. In others, propagation first stabilizes the relevant components and the target occurrence is then fixed by the corresponding connective table. Consistency is not a second basic notion of justification but a distinguished property of certain justified outcomes. The article establishes local and global soundness, conservativity over the classical fragment, and a conditional adequacy result. It further develops a translation between decomposed formulas and informational graphs, with a reverse reconstruction theorem for well-formed graphs. The result is a unified operational account of first-order reasoning situated between model-theoretic and proof-theoretic approaches, in which semantics, propagation, and graphical structure are mutually supporting rather than independently layered. Full article
(This article belongs to the Special Issue 15th Anniversary of Axioms: Logic)
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31 pages, 1135 KB  
Article
Intuitionistic Fuzzy Decision Tree Temporal Logic and Its Application in Engineering Decision-Making
by Xianfeng Yu, Jianhua Zhao, Famin Ma, Lei Wang and Huirong Li
Axioms 2026, 15(6), 456; https://doi.org/10.3390/axioms15060456 - 18 Jun 2026
Viewed by 229
Abstract
This paper investigates engineering decision optimization in uncertain environments. Subject to constraints on cost and expected returns, engineering decisions optimize material input, equipment selection and process arrangement to minimize costs and maximize economic benefits. As an efficient formal verification technique, model checking offers [...] Read more.
This paper investigates engineering decision optimization in uncertain environments. Subject to constraints on cost and expected returns, engineering decisions optimize material input, equipment selection and process arrangement to minimize costs and maximize economic benefits. As an efficient formal verification technique, model checking offers a new approach to addressing this problem. Traditional model checking focuses on qualitative verification, while quantitative approaches, including probabilistic and possibilistic model checking, have been gradually developed. Among them, possibilistic model checking is more applicable to systems with fuzzy uncertainty. However, existing possibilistic model-checking techniques have notable limitations: they are only designed for closed systems and ignore interactions between the system and external environments; their simplistic information aggregation leads to information asynchrony and loss; and they cannot model and verify systems with incomplete information. Model checking based on possibilistic decision processes enables the selection of uncertain actions and initially resolves the modeling and verification of open systems. In our previous work, we introduced quality constraints into possibilistic temporal logic to mitigate information asynchrony and loss. We also established the theories of intuitionistic fuzzy Kripke structure (IFKS) and Intuitionistic Fuzzy Computation Tree Logic (IFCTL), which support the modeling and verification of systems with incomplete information. To improve the practicality and accuracy of engineering decisions, this study adopts the ideas of uncertain decision-making behavior selection, quality constraints and incomplete information modeling. It extends IFKS to the Weighted Intuitionistic Fuzzy Kripke Structure (WIFKS) and evolves IFCTL into the intuitionistic fuzzy decision tree logic (IFDTL). We further propose an IFDTL model-checking algorithm and a multi-attribute engineering decision algorithm based on the proposed method, along with corresponding correctness proofs and complexity analysis. A case study on Qinling health-preserving tourism planning verifies the rationality and effectiveness of the presented approach. This research provides a novel formal solution for engineering decision-making under uncertainty. Full article
(This article belongs to the Special Issue 15th Anniversary of Axioms: Logic)
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