Chapter 5 extends the analysis to modal vocabulary and, in particular, reconstructs Kripkean semantics for
modal logic in incompatibility semantics.
One might argue that, although classical
modal logic adequately models metaphysical modality in most instances, there are certain cases where it breaks down and ceases to accurately capture metaphysical necessity and metaphysical possibility.
The paper extends the fuzzy
modal logic [1,2, and 4], fuzzy enviromnent [3] and neutrosophic sets, numbers and operators [5-12], together with the last developments of the neutrosophic enviromnent {including (t, i, f)-neutrosophic algebraic structures, neutrosophic triplet structures, and neutrosophic overset / underset / offset} [13-15] passing through the symbolic neutrosophic logic [16], ultimately to neutrosophic
modal logic.
This implies that the
modal logic S4 is complete in any metric separable dense-in-itself space, for example, [R.sup.n].
(1) Professor of Philosophy, University of Chicago; author, Abriss der Logittik (1929), Logische Syntax der Spracbe (1934, published in English in 1937 as The Logical Syntax of Language), Philosophy and Logical Syntax (1935), Foundations of Logic and Mathematics (1939), Introduction to Semantics (1942), Formalization of Logic (1943), Meaning and Necessity: A Study in Semantics and
Modal Logic (1947).
Among the topics are Barcan Marcus' courageous philosophical life and work, a philosopher's calling, Barcan formulas in second-order
modal logic, whether identity is a functional property, Barcan Marcus on believing without a language, and moral dilemmas from a logical and from a moral point of view.
Tony Street's study of Avicenna's
modal logic is a further stage in his collaboration with Paul Thom in understanding the significance of this area of thought and particularly in seeing the connection between logic and metaphysics in the Avicennan corpus.
A Completeness Theorem in
Modal Logic. In Journal of Symbolic Logic, 1959, vol.
From this perspective it is worth mentioning that contemporary
modal logic, discussed in the essay of Sanford Shieh (Chapter 13, 'Logic, Modality, and Metaphysics in Early Analytic Philosophy: C.I.