This paper specifies classes of framesmaximally omnitemporally characteristic for Thomas' normal modal logicT 2 + and for each logic in the ascending chain of Segerberg logics investigated by Segerberg and Hughes and Cresswell. It is shown that distinct a,scending chains of generalized Segerberg logics can be constructed from eachT n + logic (n 2). The set containing allT n + and Segerberg logics can be totally- (linearly-) ordered but not well-ordered by the inclusion relation. The order type of this ordered (...) set is *( + 1). Throughout the paper my approach is fundamentally semantical. (shrink)

Der Ausdruck "Soziotektonik" bezeichnet das Netzwerk menschlicher Wechselwirkungen, welche durch Symbole und Signale übermittelt werden und die Koordination und Integration verschiedener Sozialsysteme ermöglichen. Jedes Sozialnetzwerk ist zeitbedingt und seine Evolution ist das Ergebnis menschlicher Entscheidungen. Die Entwicklung kann im Rückblick beschrieben werden; im Vorausblick können nur Wahrscheinlichkeitsaussagen gemacht werden. Die Teilsysteme sind nicht hierarchisch untergeordnet, sondern heterarchisch beigeordnet und unterliegen infolgedessen unvereinbaren Einflüssen. Der Grad der möglichen Harmonisierung kann mathematisch-topologisch formuliert werden.

The paper concerns time, change and contradiction, and is in three parts. The first is an analysis of the problem of the instant of change. It is argued that some changes are such that at the instant of change the system is in both the prior and the posterior state. In particular there are some changes from p being true to p being true where a contradiction is realized. The second part of the paper specifies a formal logic which accommodates (...) this possibility. It is a tense logic based on an underlying paraconsistent prepositional logic, the logic of paradox. (See the author's article of the same name Journal of Philosophical Logic 8 (1979).) Soundness and completeness are established, the latter by the canonical model construction, and extensions of the basic system briefly considered. The final part of the paper discusses Leibniz's principle of continuity: Whatever holds up to the limit holds at the limit. It argues that in the context of physical changes this is a very plausible principle. When it is built into the logic of the previous part, it allows a rigorous proof that change entails contradictions. Finally the relation of this to remarks on dialectics by Hegel and Engels is briefly discussed. (shrink)

In this article, I offer two different formalizations for prescriptions which correspond to two different forms of biblical prohibitions. I discuss the known fact that the prohibitive commandments of the Decalogue according to the Septuagint and the Vulgate, Exodus 20 and Deuteronomy 5, are formulated with normative future tense indicatives. However, the Greek and Latin sources provide in Mark 10:19 variants of five biblical prohibitive commandments which are formulated with prohibitive subjunctives. I argue that there are semantic differences between normative (...) future tense indicatives and prohibitive subjunctives. These semantic differences are of importance for the understanding of the Decalogue. (shrink)

Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can force the existence of infinite models and have undecidable satisfiability (...) problems. (shrink)