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Semantic Tableau Versions of Some Normal Modal Systems with Propositional Quantifiers
Stockholm University, Faculty of Humanities, Department of Philosophy.
Number of Authors: 12019 (English)In: Organon F, ISSN 1335-0668, Vol. 26, no 3, p. 505-536Article in journal (Refereed) Published
Abstract [en]

In Symbolic Logic (1932), C. I. Lewis developed five modal systems S1 - S5. S4 and S5 arc so-called normal modal systems. Since Lewis and La.ngford's pioneering work many other systems of this kind have been investigated, among them the 32 systems that can be generated by the five axioms T, D, B, 4 and 5. Lewis also discusses how his systems can be augmented by propositional quantifiers and how these augmented logics allow us to express some interesting ideas that cannot be expressed in the corresponding quantifier-free logics. In this paper, I will develop 64 normal modal semantic tableau systems that can be extended by propositional quantifiers yielding 64 extended systems. All in all, we will investigate 128 different systems. I will show how these systems can be used to prove some interesting theorems and I will discuss Lewis's so-called existence postulate and some of its consequences. Finally, I will prove that all normal modal systems are sound and complete and that all systems (including the extended systems) are sound with respect to their semantics. It is left as an open question whether or not the extended systems are complete.

Place, publisher, year, edition, pages
2019. Vol. 26, no 3, p. 505-536
Keywords [en]
C. I. Lewis, Modal logic, Propositional quantifiers, Semantic tableaux
National Category
Philosophy, Ethics and Religion
Identifiers
URN: urn:nbn:se:su:diva-175890DOI: 10.31577/orgf.2019.26309ISI: 000491216800009OAI: oai:DiVA.org:su-175890DiVA, id: diva2:1373453
Available from: 2019-11-27 Created: 2019-11-27 Last updated: 2019-11-27Bibliographically approved

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