Combining Logics and Theories

A special issue of Logics (ISSN 2813-0405).

Deadline for manuscript submissions: closed (10 November 2023) | Viewed by 1864

Special Issue Editors


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Guest Editor
Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Interests: logics and theories and their combination (e.g., meet, importing, fibring); properties of logics and their preservation, including decidability; deductive systems; evidence, probability, and quantum logics
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Interests: logics and theories and their combination (e.g., meet, importing, fibring); preservation of properties of logics and theories under combination; proof theory; evidence, probability, and quantum logics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Despite the great variety of logics that exist nowadays, it is not common to find a logic allowing for reasoning with several concepts simultaneously, such as time, space, belief, knowledge, necessity, possibility, obligation and action, among others.  A similar phenomenon occurs when working with theories. Although this specialization allows each logic/theory to capture with great precision the envisaged concept, in most of the cases, it requires that we work with several notions at the same time. The pioneering works on combining logics and theories can be traced back to the studies of Barwise in 1974 and to Thompson, Janiczak and Rogers in 1952-1956 on categorical relationships between logics and on the combination of theories, respectively. Since then, there have been significant research efforts in both fronts. Several mechanisms have been proposed for combining logics, such as products of modal logics (Shekhtman 1978), fusion (Thomason 1980) and fibring (Gabbay 1992), together with preservation results. At the forefront of theories is the combination mechanism, demonstrating excellent joining and preservation results, having been established by Pigozzi in 1974 and elaborated by Nelson and Oppen in 1979.

This Special Issue aims to gather high-quality papers presenting various combinations of logics and theories and their applications.

Original research articles and reviews are welcome. Research areas may include:

  • Applications of combinations of logics/theories to the sciences, law and philosophy;
  • Categorial and algebraic accounts of the combination of logics and theories;
  • Combinations and modularity in ontologies;
  • Combinations and modularity in term rewriting;
  • Combination methods in automated reasoning;
  • Combination of data types;
  • Combination of logics ;
  • Combination of theories;
  • Deductive systems for combination;
  • Institutions and combination;
  • Preservation results;
  • Products of logics;
  • Satisfiability modulo theories.

Prof. Dr. Cristina Sernadas
Dr. João Rasga
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. Logics is an international peer-reviewed open access quarterly 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 1000 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

  • applications of combinations of logics/theories to the sciences, law and philosophy
  • categorial and algebraic accounts of the combination of logics and theories
  • combinations and modularity in ontologies
  • combinations and modularity in term rewriting
  • combination methods in automated reasoning
  • combination of data types
  • combination of logics
  • combination of theories
  • deductive systems for combination
  • preservation results

Published Papers (1 paper)

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Research

58 pages, 772 KiB  
Article
Graph Algebras and Derived Graph Operations
by Uwe Wolter and Tam T. Truong
Logics 2023, 1(4), 182-239; https://doi.org/10.3390/logics1040010 - 17 Oct 2023
Viewed by 1119
Abstract
We revise our former definition of graph operations and correspondingly adapt the construction of graph term algebras. As a first contribution to a prospective research field, Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To [...] Read more.
We revise our former definition of graph operations and correspondingly adapt the construction of graph term algebras. As a first contribution to a prospective research field, Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To tackle this generalization task, we revise and reformulate traditional set-theoretic definitions, constructions and proofs in Universal Algebra by means of more category-theoretic concepts and constructions. In particular, we generalize the concept of generated subalgebra and prove that all monomorphic homomorphisms between graph algebras are regular. Derived graph operations are the other main topic. After an in-depth analysis of terms as representations of derived operations in traditional algebras, we identify three basic mechanisms to construct new graph operations out of given ones: parallel composition, instantiation, and sequential composition. As a counterpart of terms, we introduce graph operation expressions with a structure as close as possible to the structure of terms. We show that the three mechanisms allow us to construct, for any graph operation expression, a corresponding derived graph operation in any graph algebra. Full article
(This article belongs to the Special Issue Combining Logics and Theories)
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