Next Article in Journal
Tenth Volume of Axioms and Why Axioms Was Launched
Previous Article in Journal
Some New Observations for F-Contractions in Vector-Valued Metric Spaces of Perov’s Type
Article

Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics

by 1,2
1
Center for Logic and Philosophy of Science, KU Leuven, 3000 Leuven, Belgium
2
KU Leuven Institute for Artificial Intelligence, KU Leuven, 3000 Leuven, Belgium
Academic Editor: Radko Mesiar
Axioms 2021, 10(3), 128; https://doi.org/10.3390/axioms10030128
Received: 28 April 2021 / Revised: 9 June 2021 / Accepted: 17 June 2021 / Published: 22 June 2021
Aristotelian diagrams, such as the square of opposition, are well-known in the context of normal modal logics (i.e., systems of modal logic which can be given a relational semantics in terms of Kripke models). This paper studies Aristotelian diagrams for non-normal systems of modal logic (based on neighborhood semantics, a topologically inspired generalization of relational semantics). In particular, we investigate the phenomenon of logic-sensitivity of Aristotelian diagrams. We distinguish between four different types of logic-sensitivity, viz. with respect to (i) Aristotelian families, (ii) logical equivalence of formulas, (iii) contingency of formulas, and (iv) Boolean subfamilies of a given Aristotelian family. We provide concrete examples of Aristotelian diagrams that illustrate these four types of logic-sensitivity in the realm of normal modal logic. Next, we discuss more subtle examples of Aristotelian diagrams, which are not sensitive with respect to normal modal logics, but which nevertheless turn out to be highly logic-sensitive once we turn to non-normal systems of modal logic. View Full-Text
Keywords: Aristotelian diagram; non-normal modal logic; square of opposition; logical geometry; neighborhood semantics; bitstring semantics Aristotelian diagram; non-normal modal logic; square of opposition; logical geometry; neighborhood semantics; bitstring semantics
Show Figures

Figure 1

MDPI and ACS Style

Demey, L. Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics. Axioms 2021, 10, 128. https://doi.org/10.3390/axioms10030128

AMA Style

Demey L. Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics. Axioms. 2021; 10(3):128. https://doi.org/10.3390/axioms10030128

Chicago/Turabian Style

Demey, Lorenz. 2021. "Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics" Axioms 10, no. 3: 128. https://doi.org/10.3390/axioms10030128

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop