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Mathematics
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Logic and Computation
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Logic and Computation

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 9365

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Răzvan Diaconescu

E-Mail Website
Guest Editor
Simion Stoilow Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania
Interests: model theory and category theory as such and with applications to computing; experimental mathematics; formal specification and verification

Special Issue Information

Dear Colleagues,

Logic and computation are highly interdependent areas of research. On one hand, logic plays an important role in computation both at the foundational and at the applied levels. For instance, several well-known programming and specification languages and systems have been developed as computational implementations of logical systems. Computing paradigms such as declarative programming or formal specification and verification owe much to logic. On the other hand. there is a lot of computing-driven research in logic. Since the last century, many important developments in logic have happened in relation to computation. For instance, modern areas of logic such as higher order logic or the axiomatic approach to model theory (e.g., the institution theory of Goguen and Burstall) are very much driven by computing motivations.

This Special Issue dedicated to logic and computation invites submissions of papers that address any aspect of the rather complex and broad relationship between the two areas.

Prof. Dr. Răzvan Diaconescu
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 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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • higher order logic
  • fuzzy logic
  • type theory
  • institution theory
  • formal specification
  • formal verification
  • logic programming
  • functional programming
  • theorem proving

Published Papers (5 papers)

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Research

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21 pages, 355 KiB  
Article
Representing 3/2-Institutions as Stratified Institutions
by Răzvan Diaconescu
Mathematics 2022, 10(9), 1507; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091507 - 01 May 2022
Cited by 4 | Viewed by 1079
Abstract
On the one hand, the extension of ordinary institution theory, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of the models. On the other hand, the theory of [...] Read more.
On the one hand, the extension of ordinary institution theory, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of the models. On the other hand, the theory of 3/2-institutions is an extension of ordinary institution theory that accommodates the partiality of the signature morphisms and its syntactic and semantic effects. The latter extension is motivated by applications to conceptual blending and software evolution. In this paper, we develop a general representation theorem of 3/2-institutions as stratified institutions. This enables a transfer of conceptual infrastructure from stratified to 3/2-institutions. We provide some examples in this direction. Full article
(This article belongs to the Special Issue Logic and Computation)
65 pages, 881 KiB  
Article
Logics of Statements in Context-Category Independent Basics
by Uwe Wolter
Mathematics 2022, 10(7), 1085; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071085 - 28 Mar 2022
Cited by 1 | Viewed by 1381
Abstract
Based on a formalization of open formulas as statements in context, the paper presents a freshly new and abstract view of logics and specification formalisms. Generalizing concepts like sets of generators in Group Theory, underlying graph of a sketch in Category Theory, sets [...] Read more.
Based on a formalization of open formulas as statements in context, the paper presents a freshly new and abstract view of logics and specification formalisms. Generalizing concepts like sets of generators in Group Theory, underlying graph of a sketch in Category Theory, sets of individual names in Description Logic and underlying graph-based structure of a software model in Software Engineering, we coin an abstract concept of context. We show how to define, in a category independent way, arbitrary first-order statements in arbitrary contexts. Examples of those statements are defining relations in Group Theory, commutative, limit and colimit diagrams in Category Theory, assertional axioms in Description Logic and constraints in Software Engineering. To validate the appropriateness of the newly proposed abstract framework, we prove that our category independent definitions and constructions give us a very broad spectrum of Institutions of Statements at hand. For any Institution of Statements, a specification (presentation) is given by a context together with a set of first-order statements in that context. Since many of our motivating examples are variants of sketches, we will simply use the term sketch for those specifications. We investigate exhaustively different kinds of arrows between sketches and their interrelations. To pave the way for a future development of category independent deduction calculi for sketches, we define arbitrary first-order sketch conditions and corresponding sketch constraints as a generalization of graph conditions and graph constraints, respectively. Sketch constraints are the crucial conceptual tool to describe and reason about the structure of sketches. We close the paper with some vital observations, insights and ideas related to future deduction calculi for sketches. Moreover, we outline that our universal method to define sketch constraints enables us to establish and to work with conceptual hierarchies of sketches. Full article
(This article belongs to the Special Issue Logic and Computation)
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35 pages, 15592 KiB  
Article
Supervised Learning Perspective in Logic Mining
by Mohd Shareduwan Mohd Kasihmuddin, Siti Zulaikha Mohd Jamaludin, Mohd. Asyraf Mansor, Habibah A. Wahab and Siti Maisharah Sheikh Ghadzi
Mathematics 2022, 10(6), 915; https://0-doi-org.brum.beds.ac.uk/10.3390/math10060915 - 13 Mar 2022
Cited by 44 | Viewed by 2469
Abstract
Creating optimal logic mining is strongly dependent on how the learning data are structured. Without optimal data structure, intelligence systems integrated into logic mining, such as an artificial neural network, tend to converge to suboptimal solution. This paper proposed a novel logic mining [...] Read more.
Creating optimal logic mining is strongly dependent on how the learning data are structured. Without optimal data structure, intelligence systems integrated into logic mining, such as an artificial neural network, tend to converge to suboptimal solution. This paper proposed a novel logic mining that integrates supervised learning via association analysis to identify the most optimal arrangement with respect to the given logical rule. By utilizing Hopfield neural network as an associative memory to store information of the logical rule, the optimal logical rule from the correlation analysis will be learned and the corresponding optimal induced logical rule can be obtained. In other words, the optimal logical rule increases the chances for the logic mining to locate the optimal induced logic that generalize the datasets. The proposed work is extensively tested on a variety of benchmark datasets with various performance metrics. Based on the experimental results, the proposed supervised logic mining demonstrated superiority and the least competitiveness compared to the existing method. Full article
(This article belongs to the Special Issue Logic and Computation)
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23 pages, 488 KiB  
Article
Representation and Reasoning about Strategic Abilities with ω-Regular Properties
by Liping Xiong and Sumei Guo
Mathematics 2021, 9(23), 3052; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233052 - 27 Nov 2021
Viewed by 1643
Abstract
Specification and verification of coalitional strategic abilities have been an active research area in multi-agent systems, artificial intelligence, and game theory. Recently, many strategic logics, e.g., Strategy Logic (SL) and alternating-time temporal logic (ATL*), have been proposed based on classical temporal [...] Read more.
Specification and verification of coalitional strategic abilities have been an active research area in multi-agent systems, artificial intelligence, and game theory. Recently, many strategic logics, e.g., Strategy Logic (SL) and alternating-time temporal logic (ATL*), have been proposed based on classical temporal logics, e.g., linear-time temporal logic (LTL) and computational tree logic (CTL*), respectively. However, these logics cannot express general ω-regular properties, the need for which are considered compelling from practical applications, especially in industry. To remedy this problem, in this paper, based on linear dynamic logic (LDL), proposed by Moshe Y. Vardi, we propose LDL-based Strategy Logic (LDL-SL). Interpreted on concurrent game structures, LDL-SL extends SL, which contains existential/universal quantification operators about regular expressions. Here we adopt a branching-time version. This logic can express general ω-regular properties and describe more programmed constraints about individual/group strategies. Then we study three types of fragments (i.e., one-goal, ATL-like, star-free) of LDL-SL. Furthermore, we show that prevalent strategic logics based on LTL/CTL*, such as SL/ATL*, are exactly equivalent with those corresponding star-free strategic logics, where only star-free regular expressions are considered. Moreover, results show that reasoning complexity about the model-checking problems for these new logics, including one-goal and ATL-like fragments, is not harder than those of corresponding SL or ATL*. Full article
(This article belongs to the Special Issue Logic and Computation)
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Review

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33 pages, 488 KiB  
Review
The Axiomatic Approach to Non-Classical Model Theory
by Răzvan Diaconescu
Mathematics 2022, 10(19), 3428; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193428 - 21 Sep 2022
Viewed by 1397
Abstract
Institution theory represents the fully axiomatic approach to model theory in which all components of logical systems are treated fully abstractly by reliance on category theory. Here, we survey some developments over the last decade or so concerning the institution theoretic approach to [...] Read more.
Institution theory represents the fully axiomatic approach to model theory in which all components of logical systems are treated fully abstractly by reliance on category theory. Here, we survey some developments over the last decade or so concerning the institution theoretic approach to non-classical aspects of model theory. Our focus will be on many-valued truth and on models with states, which are addressed by the two extensions of ordinary institution theory known as L-institutions and stratified institutions, respectively. The discussion will include relevant concepts, techniques, and results from these two areas. Full article
(This article belongs to the Special Issue Logic and Computation)
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