Einleitung.--Die begriffliche Erkenntniss der Körperwelt.--Natur und Geist.--Natur und Geschichte.--Die historische Begriffsbildung.--Naturphilosophie und Geschichts-Philosophie.

In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds (...) model validating precisely the same formulas (of the language in question). (shrink)

PREFACE TO THE FIRST FEENCH EDITION. WHEN the Emperor Otho IIL visited the tomb in which had reposed for many years the mortal remains of Charlemagne, ...

Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number (...) of simple observations is made showing that the unwanted phenomenon exemplified by tonk in some logics also occurs in contexts in which tonk is acceptable. In fact, in any non-trivial context, the acceptance of arbitrary introduction rules for logical operations permits operations leading to triviality. Connectives that in all non-trivial contexts lead to triviality will be called non-trivially trivializing connectives. (shrink)

Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.

Jiva.--Samsara.--Karman.--Naman und Brahman.--Yoga.--Prajna paramita.--Trivarga. Schakti. Maya.

FRIELING: HARMONIE UND RHYTHMUS IN NATUR UND KUNST.

1. t. Musikalische elemente und elementargebilde.--2. t. Beethovens d-moll-sonate (op. 31, erster satz).

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to (...) be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. (shrink)