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Logics, Volume 2, Issue 1 (March 2024) – 3 articles

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48 pages, 6809 KiB  
Article
Modelling Value-Oriented Legal Reasoning in LogiKEy
by Christoph Benzmüller, David Fuenmayor and Bertram Lomfeld
Logics 2024, 2(1), 31-78; https://doi.org/10.3390/logics2010003 - 14 Mar 2024
Viewed by 453
Abstract
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
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20 pages, 1742 KiB  
Article
Projective Geometry as a Model for Hegel’s Logic
by Paul Redding
Logics 2024, 2(1), 11-30; https://doi.org/10.3390/logics2010002 - 22 Jan 2024
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Abstract
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
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10 pages, 633 KiB  
Article
On Line Diagrams Plus Modality
by J.-Martín Castro-Manzano
Logics 2024, 2(1), 1-10; https://doi.org/10.3390/logics2010001 - 20 Dec 2023
Viewed by 509
Abstract
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
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