We present a pole expansion for the propagators in the framework of normalized quantum electrodynamics and compare it with the more canonical results from S-matrix theory.

In the modal literature various notions of "completeness" have been studied for normal modal logics. Four of these are defined here, viz. completeness, first-order completeness, canonicity and possession of the finite model property -- and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability and (...) preservation under ultrafilter extensions are introduced and studied as well. (shrink)

After having defined the KARO logic for specifying intelligent agents in earlier work we now turn to the question how to realise agents specified in the KARO framework. To this end we look at agent programming languages that we have defined, and investigate how programs in these languages can be linked to the KARO logic.

We give in this paper a sufficient condition, cast in semantic terms, for Hallden-completeness in normal modal logics, a modal logic being said to be Hallden-complete (or Ήallden-reasonable') just in case for any disjunctive formula provable in the logic, where the disjuncts have no propositional variables in common, one or other of those disjuncts is provable in the logic.

This collection of essays delineates the history of the rather disparate intellectual tradition usually labeled as "Platonic" or "Neoplatonic". In chronological order, the book covers the most eminent philosophic schools of thought within that tradition. The most important terms of the Platonic tradition are studied together with a discussion of their semantic implications, the philosophical and theological claims associated with the terms, the sources that furnish the terms, and the intellectual traditions aligned with or opposed to them. The contributors thereby (...) provide a vivid intellectual map of the Middle Ages and the Early Modern period. Contributions are written in English or German. (shrink)

This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around (...) 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality. (shrink)

In this paper thecanonicalmodal logics, a kind of complete modal logics introduced in K. Fine [4] and R. I. Goldblatt [5], will be characterized semantically using the concept of anultrafilter extension, an operation on frames inspired by the algebraic theory of modal logic. Theorem 8 of R. I. Goldblatt and S. K. Thomason [6] characterizing the modally definable Σ⊿-elementary classes of frames will follow as a corollary. A second corollary is Theorem 2 of [4] which states that any complete modal (...) logic defining a Σ⊿-elementary class of frames is canonical.The main tool in obtaining these results is the duality between modal algebras and general frames developed in R. I. Goldblatt [5]. The relevant notions and results from this theory will be stated in §2. The concept of a canonical modal logic is introduced and motivated in §3, which also contains the above-mentioned theorems. In §4, a kind of appendix to the preceding discussion, preservation of first-order sentences under ultrafilter extensions is discussed.The modal language to be considered here has an infinite supply of proposition letters, a propositional constant ⊥, the usual Boolean operators ¬, ∨, ∨, →, and ↔ —with ¬ and ∨ regarded as primitives—and the two unary modal operators ◇ and □ — ◇ being regarded as primitive. Modal formulas will be denoted by lower case Greek letters, sets of formulas by Greek capitals. (shrink)

Ook al staan de beelden van Confucius, Lao Zi en Boeddha in sommige Chinese tempels weer broederlijk bijeen op het altaar, hun verschillende wegen tot zelfcultivering worden zelden in onderlinge samenhang beschreven. Dit boek benadert confucianisme, daoïsme en het Chinese boeddhisme in zijn vroege ontwikkeling vanuit hun visie op de praktijk van de zelfcultivering. Hoewel ze een volstrekt ander doel hebben dan de westerse zelfverwerkelijking, mogen de Chinese wegen zich in onze contreien toch in een grote populariteit verheugen. Omdat de (...) zelfcultivering in China primair gericht is op de emoties, vormt de emotiecultivering de rode draad in dit boek. Het begrip Qi, levenskracht, speelt een grote rol in alle cultiveringspraktijken en staat centraal in het klassieke Chinese denken. Het eerste hoofdstuk biedt een inleiding in dit begrip, waardoor de lezer een overzicht krijgt van een aantal Chinese kernconcepten en theorieën en daarmee ook van de context van de emotiecultivering. Naast de beschrijving daarvan in confucianisme, daoïsme en boeddhisme biedt het boek verder een beschouwing van de Chinese landschapsschilderkunst als "filosoferen met het penseel". Het slothoofdstuk vat de verschillende cultiveringspraktijken samen en presenteert ze onder de noemer van Wegen naar het Midden. (shrink)

The existence of various physical phenomena stems from the concept called asymptotic emergence, that is, they seem to be exclusively reserved for certain limiting theories. Important examples are spontaneous symmetry breaking (SSB) and phase transitions: these would only occur in the classical or thermodynamic limit of underlying finite quantum systems, since for finite quantum systems, due to the uniqueness of the relevant states, such phenomena are excluded by Theory. In Nature, however, finite quantum systems describing real materials clearly exhibit such (...) effects. In this paper we discuss these apparently “paradoxical” phenomena and outline various ideas and mechanisms that encompass both theory and reality, from physical and mathematical points of view. (shrink)

This book compares Chinese thought to that of the West. With recent Western interest in Chinese Buddhism (also known as Zen) and Daoism an understanding of their underlying ways of thinking is crucial for approaching them properly. The topics treated include worldview, world -- man relation, and mind and consciousness. A unique feature of the book is the comparison between Daoism and Chinese Buddhism on the one hand, and the Greek schools of Epicureanism and Stoicism on the other. A remarkable (...) similarity as well as a significant difference is found between these ways of life. In both China and Greece they learned how to live in the 'Now'. But in China this is centred around the body, while in Greece this was a strictly rational pursuit. The main differences between the Chinese and Western ways can be summarised in the words 'accord' and 'separation'. Clearly, in East and West different roads have been, and still are walked. Yet, these roads do not inevitably entail different ways of life. 'Walking two roads at once' (Zhuangzi) it is possible to go beyond accord and separation. (shrink)