Building on the recent scholarship of Bonnie Kent, Christian Trottmann, and especially L.M. de Rijk, this volume gathers together studies by other specialists on Odonis, covering his ideas in economics, logic, metaphysics, ethics, natural ...

The strong connection between the two and its development into the Middle Ages form a major subject of this volume.Other themes featuring in this book are Plato ...

For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding algebras. (...) Taken together, these properties imply that results about a Sahlqvist variety V van be obtained by reasoning in the elementary class of canonical structures of algebras in V.We give an example of this strategy in the variety of Cylindric Algebras: we show that an important identity calledHenkin's equation is equivalent to a simpler identity that uses only one variable. We give a conceptually simple proof by showing that the first-order correspondents of these two equations are equivalent over the class of cylindric atom structures. (shrink)

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.

Paperback. This volume is a new interpretation of Plato's earlier and later Theory of Ideas, starting from a detailed analysis of the dialogue, The Sophist.The way in which Plato announces his novel Metaphysics has been puzzling scholars for a long time. Did Plato really introduce Change into the Transcendent World and thus abandon his Theory of Unchangeable Forms?Many of Plato's commentators have claimed that the use of modern techniques of logico-semantical analysis can be a valuable aid in unravelling this problem, (...) as well as other difficulties Plato raised and attempted to solve. In this commentary, Plato's own logico-semantical approach to metaphysical problems is followed. (shrink)

This article argues in favour of voluntary active euthanasia in human beings on the grounds that we (society in general) perform euthanasia on valued companion animals when their suffering is considered great. I argue that suffering is a morally relevant criterion that should be considered in all cases (human and animal) of euthanasia. I further argue that human beings possess autonomy, a morally relevant difference to companion animals, that allows them to reason about their futures in a way that animals (...) cannot, which gives us more reason to grant euthanasia, if requested autonomously by terminally ill patients who are experiencing extreme suffering. I consider objections around the sanctity of human life and sufficient palliation. I argue that neither of these objections give sufficient reason to deny competent human beings euthanasia if autonomously requested. (shrink)

This chapter contains sections titled: Introduction Model Theory Proof Theory Modal Predicate Logic.

Each inhabitant of our world Gilbert calls an id quod est or subsistens. Its main constituents are the subsistentiae and these are accompanied by the 'accidents', quantity and quality. The subsistent owes its status to a collection of inferior members of the Aristotelian class of accidents, which to Gilbert 's mind are rather 'accessories' or 'attachments from without'. The term 'substantia' is used both to stand for substance and substantial form, i.e., that by which something is subsistent. The collection of (...) subsistentiae or the forma totius is called natura. However, 'natura' is also used to stand for either just one subsistentia or all the forms found in a subsistens even including its 'accidental' forms. The inclusion of all kinds of accidents is seldom found in the intension of the word 'natura'. One of the key notions featuring in Gilbert 's ontology is esse aliquid. 'To be a-something' has a threefold import. First, it means 'to be only some thing', and to miss perfection. Second, it has the positive sense of 'being a something', i.e. 'being determinate and well-delineated', not indefinite, not formless that is. Third, 'to be a something' implies concreteness, corporealness and singularity. (shrink)

Intensional logic has emerged, since the 1960' s, as a powerful theoretical and practical tool in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy and even the foundations of mathematics. The present volume is a collection of carefully chosen papers, giving the reader a taste of the frontline state of research in intensional logics today. Most papers are representative of new ideas and/or new research themes. The collection would benefit the researcher as well as the student. This book (...) is a most welcome addition to our series. The Editors CONTENTS PREFACE IX JOHAN VAN BENTHEM AND NATASHA ALECHINA Modal Quantification over Structured Domains PATRICK BLACKBURN AND WILFRIED MEYER-VIOL Modal Logic and Model-Theoretic Syntax 29 RUY J. G. B. DE QUEIROZ AND DOV M. GABBAY The Functional Interpretation of Modal Necessity 61 VLADIMIR V. RYBAKOV Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic 93 JERRY SELIGMAN The Logic of Correct Description 107 DIMITER VAKARELOV Modal Logics of Arrows 137 HEINRICH WANSING A Full-Circle Theorem for Simple Tense Logic 173 MICHAEL ZAKHARYASCHEV Canonical Formulas for Modal and Superintuitionistic Logics: A Short Outline 195 EDWARD N. ZALTA 249 The Modal Object Calculus and its Interpretation NAME INDEX 281 SUBJECT INDEX 285 PREFACE Intensional logic has many faces. In this preface we identify some prominent ones without aiming at completeness. (shrink)

We consider some modal languages with a modal operator $D$ whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at.

We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief discussion of the wider applicability of our ideas.

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems (...) and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. (shrink)

In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations (...) from relation algebra. In addition, the logic has devices for expressing whether in a given state a certain instruction can be carried out, and whether that state can be arrived at by carrying out a certain instruction.This paper deals mainly with technical aspects of our dynamic modal logic. It gives an exact description of the expressive power of this language; it also contains results on decidability for the language with arbitrary structures and for the special case with a restricted class of admissible structures. In addition, a complete axiomatization is given. The paper concludes with a remark about the modal algebras appropriate for our dynamic modal logic, and some questions for further work. (shrink)

v. 1. On the twelfth century theories of fallacy.--v. 2. The origin and early development of the theory of supposition.

Wijsgerige bezinning op de rol en betekenis van religie in het debat over normen en waarden.

v. 1. General introduction, the works on logic -- v. 2. The metaphysics, semantics in Aristotle's strategy of argument.

The idea of combining logics, structures, and theories has recently been attracting interest in areas as diverse as constraint logic programming, theorem proving, verification, computational linguistics, artificial intelligence and indeed, various branches of logic itself. It would be an exaggeration to claim that these (scattered, and by-and-large independent) investigations have crystallized into an enterprise meriting the title "combined methods"; nonetheless, a number of interesting themes are emerging. This introduction notes some prominent ones and relates them to the papers in this (...) special issue. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.