Journal Description
Logics
Logics
is an international, peer-reviewed, open access journal on all aspects of logic published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- Recognition of Reviewers: APC discount vouchers, optional signed peer review, and reviewer names published annually in the journal.
- Companion journals for Logics include: Axioms and Mathematics.
Latest Articles
Modelling Value-Oriented Legal Reasoning in LogiKEy
Logics 2024, 2(1), 31-78; https://0-doi-org.brum.beds.ac.uk/10.3390/logics2010003 - 14 Mar 2024
Abstract
►
Show Figures
The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing, in which legal knowledge (cases and laws) is encoded by utilising context-dependent value preferences. The theory obtained is then used to formalise, automatically evaluate,
[...] Read more.
The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing, in which legal knowledge (cases and laws) is encoded by utilising context-dependent value preferences. The theory obtained is then used to formalise, automatically evaluate, and reconstruct illustrative property law cases (involving the appropriation of wild animals) within the Isabelle/HOL proof assistant system, illustrating how LogiKEy can harness interactive and automated theorem-proving technology to provide a testbed for the development and formal verification of legal domain-specific languages and theories. Modelling value-oriented legal reasoning in that framework, we establish novel bridges between the latest research in knowledge representation and reasoning in non-classical logics, automated theorem proving, and applications in legal reasoning.
Full article
Open AccessArticle
Projective Geometry as a Model for Hegel’s Logic
by
Paul Redding
Logics 2024, 2(1), 11-30; https://0-doi-org.brum.beds.ac.uk/10.3390/logics2010002 - 22 Jan 2024
Abstract
►▼
Show Figures
Recently, historians have discussed the relevance of the nineteenth-century mathematical discipline of projective geometry for early modern classical logic in relation to possible solutions to semantic problems facing it. In this paper, I consider Hegel’s Science of Logic as an attempt to provide
[...] Read more.
Recently, historians have discussed the relevance of the nineteenth-century mathematical discipline of projective geometry for early modern classical logic in relation to possible solutions to semantic problems facing it. In this paper, I consider Hegel’s Science of Logic as an attempt to provide a projective geometrical alternative to the implicit Euclidean underpinnings of Aristotle’s syllogistic logic. While this proceeds via Hegel’s acceptance of the role of the three means of Pythagorean music theory in Plato’s cosmology, the relevance of this can be separated from any fanciful “music of the spheres” approach by the fact that common mathematical structures underpin both music theory and projective geometry, as suggested in the name of projective geometry’s principal invariant, the “harmonic cross-ratio”. Here, I demonstrate this common structure in terms of the phenomenon of “inverse foreshortening”. As with recent suggestions concerning the relevance of projective geometry for logic, Hegel’s modifications of Aristotle respond to semantic problems of his logic.
Full article
Figure 1
Open AccessArticle
On Line Diagrams Plus Modality
by
J.-Martín Castro-Manzano
Logics 2024, 2(1), 1-10; https://0-doi-org.brum.beds.ac.uk/10.3390/logics2010001 - 20 Dec 2023
Abstract
►▼
Show Figures
In this paper, we produce an extension of Englebretsen’s line diagrams in order to represent modal syllogistic, i.e., we add some diagrammatic objects and rules to his system in order to reason about modal syllogistics in a diagrammatic, linear fashion.
Full article
Figure 1
Open AccessArticle
Graph Algebras and Derived Graph Operations
by
Uwe Wolter and Tam T. Truong
Logics 2023, 1(4), 182-239; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1040010 - 17 Oct 2023
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)
►▼
Show Figures
Figure 1
Open AccessArticle
Carnap’s Problem for Intuitionistic Propositional Logic
by
Haotian Tong and Dag Westerståhl
Logics 2023, 1(4), 163-181; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1040009 - 22 Sep 2023
Abstract
We show that intuitionistic propositional logic is Carnap categorical: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds with respect to the most well-known semantics relative to which intuitionistic logic is sound and
[...] Read more.
We show that intuitionistic propositional logic is Carnap categorical: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds with respect to the most well-known semantics relative to which intuitionistic logic is sound and complete; among them Kripke semantics, Beth semantics, Dragalin semantics, topological semantics, and algebraic semantics. These facts turn out to be consequences of an observation about interpretations in Heyting algebras.
Full article
Open AccessArticle
Bilateral Connexive Logic
by
Nissim Francez
Logics 2023, 1(3), 157-162; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1030008 - 4 Aug 2023
Abstract
This paper proposes a bilateral analysis of connexivity, presenting a bilateral natural deduction system for a weak connexive logic. The proposed logic deviates from other connexive logics and other bilateral logics in the following respects: (1) The logic induces a difference in meaning
[...] Read more.
This paper proposes a bilateral analysis of connexivity, presenting a bilateral natural deduction system for a weak connexive logic. The proposed logic deviates from other connexive logics and other bilateral logics in the following respects: (1) The logic induces a difference in meaning between inner and outer occurrences of negation in the connexive axioms. (2) The logic allows incoherence—assertion and denial of the same formula—while still being non-trivial.
Full article
Open AccessEssay
Why Logics?
by
Jean-Yves Beziau
Logics 2023, 1(3), 148-156; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1030007 - 5 Jul 2023
Abstract
►▼
Show Figures
In this paper we explain the different meanings of the word “logic” and the circumstances in which it makes sense to use its singular or plural form. We discuss the multiplicity of logical systems and the possibility of developing a unifying theory about
[...] Read more.
In this paper we explain the different meanings of the word “logic” and the circumstances in which it makes sense to use its singular or plural form. We discuss the multiplicity of logical systems and the possibility of developing a unifying theory about them, not itself a logical system. We undertake some comparisons with other sciences, such as biology, physics, mathematics, and linguistics. We conclude by delineating the origin, scope, and future of the journal Logics.
Full article
Figure 1
Open AccessFeature PaperArticle
Logics for Epistemic Actions: Completeness, Decidability, Expressivity
by
Alexandru Baltag, Lawrence S. Moss and Sławomir Solecki
Logics 2023, 1(2), 97-147; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1020006 - 12 Jun 2023
Abstract
►▼
Show Figures
We build and study dynamic versions of epistemic logic. We study languages parameterized by an action signature that allows one to express epistemic actions such as (truthful) public announcements, completely private announcements to groups of agents, and more. The language (Σ
[...] Read more.
We build and study dynamic versions of epistemic logic. We study languages parameterized by an action signature that allows one to express epistemic actions such as (truthful) public announcements, completely private announcements to groups of agents, and more. The language (Σ) is modeled on dynamic logic. Its sentence-building operations include modalities for the execution of programs, and for knowledge and common knowledge. Its program-building operations include action execution, composition, repetition, and choice. We consider two fragments of . In , we drop action repetition; in , we also drop common knowledge. We present the syntax and semantics of these languages and sound proof systems for the validities in them. We prove the strong completeness of a logical system for and the weak completeness of one for . We show the finite model property and, hence, decidability of . We translate into PDL, obtaining a second proof of decidability. We prove results on expressive power, comparing with modal logic together with transitive closure operators. We prove that a logical language with operators for private announcements is more expressive than one for public announcements.
Full article
Figure 1
Open AccessArticle
Concepts of Interpolation in Stratified Institutions
by
Răzvan Diaconescu
Logics 2023, 1(2), 80-96; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1020005 - 3 Apr 2023
Abstract
The extension of the (ordinary) institution theory of Goguen and Burstall, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of models. Stratified institutions cover a uniformly wide range
[...] Read more.
The extension of the (ordinary) institution theory of Goguen and Burstall, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of models. Stratified institutions cover a uniformly wide range of applications from various Kripke semantics to various automata theories and even model theories with partial signature morphisms. In this paper, we introduce two natural concepts of logical interpolation at the abstract level of stratified institutions and we provide some sufficient technical conditions in order to establish a causality relationship between them. In essence, these conditions amount to the existence of nominals structures, which are considered fully and abstractly.
Full article
Open AccessArticle
A Fundamental Non-Classical Logic
by
Wesley H. Holliday
Logics 2023, 1(1), 36-79; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1010004 - 21 Mar 2023
Cited by 2
Abstract
►▼
Show Figures
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the
[...] Read more.
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation. Finally, we discuss ways of extending these representations to lattices with a conditional or implication operation.
Full article
Figure 1
Open AccessFeature PaperArticle
Logics for Strategic Reasoning of Socially Interacting Rational Agents: An Overview and Perspectives
by
Valentin Goranko
Logics 2023, 1(1), 4-35; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1010003 - 6 Feb 2023
Abstract
►▼
Show Figures
This paper is an overview of some recent and ongoing developments of formal logical systems designed for reasoning about systems of rational agents who act in pursuit of their individual and collective goals, explicitly specified in the language as arguments of the strategic
[...] Read more.
This paper is an overview of some recent and ongoing developments of formal logical systems designed for reasoning about systems of rational agents who act in pursuit of their individual and collective goals, explicitly specified in the language as arguments of the strategic operators, in a socially interactive context of collective objectives and attitudes which guide and constrain the agents’ behavior.
Full article
Figure 1
Open AccessEditorial
From the Venerable History of Logic to the Flourishing Future of Logics
by
Valentin Goranko
Logics 2023, 1(1), 2-3; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1010002 - 21 Apr 2022
Abstract
Reasoning is one of the most important and distinguished human activities [...]
Full article
Open AccessEditorial
Publisher’s Note: Logics—A New Open Access Journal
by
Constanze Schelhorn
Logics 2023, 1(1), 1; https://0-doi-org.brum.beds.ac.uk/10.3390/logics1010001 - 16 Dec 2021
Abstract
Logic (from ancient Greek “λογικὴ τέχνη (logiké téchnē)”—“thinking art”, “procedure”) is a multidisciplinary field of research studying the formal principles of reasoning [...]
Full article
Highly Accessed Articles
Latest Books
E-Mail Alert
News
Topics
Conferences
Special Issues
Special Issue in
Logics
The Legacy of A.V. Kuznetsov in Logic, Algebra and Foundations of Mathematics
Guest Editors: Alexei Muravitsky, Alex CitkinDeadline: 31 March 2025