Let A be a formula without implications, and Γ consist of formulas containing disjunction and falsity only negatively and implication only positively. Orevkov and Nadathur proved that classical derivability of A from Γ implies intuitionistic derivability, by a transformation of derivations in sequent calculi. We give a new proof of this result , where the input data are natural deduction proofs in long normal form involving stability axioms for relations; the proof gives a quadratic algorithm to remove the stability axioms. (...) This can be of interest for computational uses of classical proofs. (shrink)

Die Abhandlung gibt eine konzentrierte Rekonstruktion der weit verstreut erschienenen Überlegungen des britisch-ungarischen Chemikers und Philosophen Michael Polanyi zur Reduktionismuskritik. Schlüssel der Kritik ist der Begriff der Grenzbedingung. Grenzbedingungen weisen auf Wirklichkeiten hin, die nicht mehr von den Gesetzmäßigkeiten der Stufe, die sie begrenzen, erreicht werden. Seine Anwendung dieses Begriffs auf Maschinen und Mechanismen ermöglicht Polanyi eine überraschende Kritik am biologischen Reduktionismus. Dieser Kritikpunkt wird durch die Entdeckung der DNA noch verstärkt.

The way physics and other parts of science work can be explained in the framework of radical constructivism. However, this constructivist view itself shows that a uniquily accepted epistemology, constructivism or any other, would not be an advantage for the developmentof science. Unlike physics some parts of science successfully use constructivist concepts inside their theories. Because this is the case particularly in learning theory, constructivist ideas can help to improve physics teaching.

From a classical proof that the gcd of natural numbers a1 and a2 is a linear combination of the two, we extract by Gödel's Dialectica interpretation an algorithm computing the coefficients. The proof uses the minimum principle. We show generally how well-founded recursion can be used to Dialectica interpret well-founded induction, which is needed in the proof of the minimum principle. In the special case of the example above it turns out that we obtain a reasonable extracted term, representing an (...) algorithm close to Euclid's. (shrink)

Jackendoff's account of relating linguistic structure and brain structure is too restricted in concentrating on formal features of computational requirements, neglecting the achievements of various types of neuroscientific modelling. My own approaches to neuronal models of syntactic organization show how these requirements could be met. The book's lack of discussion of a sound philosophy of the relation is briefly mentioned.

The papers in this series of five volumes provide a snapshot of current trends in European Cognitive Science. Each of the volumes deals with problems in cognitive science from a different perspective, covering the interacting disciplines of cognitive psychology, logic and linguistics, human-computer interaction, neuroscience and artificial intelligence respectively. Linguistics is concerned with the structure and use of languages, and logic with the form and correctness of argumentation in ordinary and scientific language. The two fields are presented with respect to (...) their role in cognitive science and artificial intelligence: How are they realised by psychological mechanisms or biological processes on the one hand or programmed or wired in machines on the other. The contributions in this volume give introductions to the state-of-the-art, emphasizing the analysis of complexity and flexibility in logic and language in the framework of classical approaches (Chapters 3, 4, 5, 7). At the same time some contributions present a broader perspective in which an integration of the formal structure with the structure of the processing systems might be possible (Chapters 2 & 6). In this context, the differences and the perspectives of the classical approaches on the one hand and of connectionist approaches on the other are compared. (Chapters 1 & 6).contributions present a broader perspective in which an integration of the formal structure with the structure of the processing systems might be possible (Chapters 2 & 6). In this context, the differences and the perspectives of the classical approaches on the one hand and of connectionist approaches on the other are compared. (Chapters 1 & 6). (shrink)

Several properties of monotone functionals (MF) and monotone majorizable functionals (MMF) used in the earlier work by the author and van de Pol are proved. It turns out that the terms of the simply typed lambda-calculus define MF, but adding primitive recursion, and even monotonic primitive recursion changes the situation: already Z.Z(1 — sg) is not MMF. It is proved that extensionality is not Dialectica-realizable by MMF, and a simple example of a MF which is not hereditarily majorizable is given.

Buchholz presented a method to build notation systems for infinite sequent-style derivations, analogous to well-known systems of notation for ordinals. The essential feature is that from a notation one can read off by a primitive recursive function its n th predecessor and, e.g. the last rule applied. Here we extend the method to the more general setting of infinite terms, in order to make it applicable in other proof-theoretic contexts as well as in recursion theory. As examples, we use the (...) method to 1. give a new proof of a well-known trade-off theorem , which says that detours through higher types can be eliminated by the use of transfinite recursion along higher ordinals, and 2. construct a continuous normalization operator with an explicit modulus of continuity. (shrink)

A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed how to construct such Kleene lattices or Kleene posets from a given distributive lattice or poset and a fixed element of (...) this lattice or poset by using the so-called twist product construction, respectively. We extend this construction of Kleene lattices and Kleene posets by considering a fixed subset instead of a fixed element. Moreover, we show that in some cases, this generating poset can be embedded into the resulting Kleene poset. We investigate the question when a Kleene poset can be represented by a Kleene poset obtained by the mentioned construction. We show that a direct product of representable Kleene posets is again representable and hence a direct product of finite chains is representable. This does not hold in general for subdirect products, but we show some examples where it holds. We present large classes of representable and non-representable Kleene posets. Finally, we investigate two kinds of extensions of a distributive poset $${\textbf{A}}$$ A, namely its Dedekind-MacNeille completion $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) and a completion $$G({\textbf{A}})$$ G ( A ) which coincides with $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) provided $${\textbf{A}}$$ A is finite. In particular we prove that if $${\textbf{A}}$$ A is a Kleene poset then its extension $$G({\textbf{A}})$$ G ( A ) is also a Kleene lattice. If the subset X of principal order ideals of $${\textbf{A}}$$ A is involution-closed and doubly dense in $$G({\textbf{A}})$$ G ( A ) then it generates $$G({\textbf{A}})$$ G ( A ) and it is isomorphic to $${\textbf{A}}$$ A itself. (shrink)

Intrinsic religiosity drives ethical consumer behavior; however, previous studies regarding this connection are limited solely to a Christian cultural context. This comparative study instead includes Christian Consumers from Germany and Moslem Consumers from Turkey to determine if a specific religious community moderates the connection between intrinsic religiosity and consumer ethics. The results show that Consumers in the Turkish, Moslem subsample, exhibit an even stronger connection between religiosity and ethical consumer behavior than Consumers from the German, Christian subsample.

Die Publikation bietet einen geschichtlichen Überblick über die Auseinandersetzung bedeutender Philosophen mit dem ältesten Problem der Philosophie: dem Leib-Seele-Problem. Wenn auch philosophischen Ursprungs, reflektieren die ausgewählten Philosophen die Bezüge zu theologischen, psychologischen, psychosomatischen, naturwissenschaftlichen und medizinischen Dimensionen dieses Problems. Im Vordergrund steht dabei die Herausarbeitung aller Aspekte des Leib-Seele-Problems. So beschäftigen sich die Herausgeber dieses Bandes mit den Fragen, ob Leib und Seele wirklich verschieden oder identisch sind, wie sie aufeinander einwirken und ob die Seele nach dem Tod weiter bestehen (...) kann. (shrink)

Das Verhältnis von Natur und Idee ist für jede idealistische Philosophie ein Kernpunkt ihres Ansatzes. Hegel bestimmte die Natur als das Andere der Idee, die sich in Freiheit als Natur aus sich entläßt. In der Natur zeigen sich die logischen Strukturen verhüllt und im Abbild, z. B. die Naturgesetze und die logischen Beziehungen. Auch die Kategorie des Lebens in Hegels Logik belegt die enge Verbindung von Natur und Logik. Die Entäußerung der Idee in der Natur gehört zum Wesen der Idee (...) auf ihrem Weg zum Geist. Diese Thematik wird in acht Beiträgen von bekannten Hegelforschern unter verschiedenen Aspekten bearbeitet. Sie verstehen die Sicht Hegels als einen bedeutenden Entwurf, der die Einheit der Wirklichkeit unter dem Vorzeichen der Idee zur Geltung bringt. (shrink)

When Professor Johannes Hoffmeister died in Bonn in 1955, a unique institution was created to continue the project he had begun - the historic-critical edition of the complete works of Hegel. This institution is known as the Hegel-Archiv.

1. Bd. Sprachanalyse, Deduktion, Induktion in Natur- und Sozialwissenschaften -- 2. Bd. Geisteswissenschaftliche Methoden: Phänomenologie, Hermeneutik und historische Methode, Dialektik -- 3. Bd. Handlungstheorie, Modallogik, Ethik, Systemtheorie.