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)

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.

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)

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)

In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) 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)

Gabbay has gathered an enormous amount of results; some of them important and novel, others important but already known, many rather routine, however. The organization of this material shows grave defects, both in the exposition and in its logical structure. Intensional logic appears as a vast collection of (often duplicated) loosely connected results. This may be a true reflection of the present state of the subject, but it does not contribute to a better understanding of it, let alone advance it.

Intensional logic is the technical study of such intensional phenomena in human reasoning as modality, knowledge, or flow of time. These all require a richer semantic picture than standard truth values in one static environment. Such a picture is provided by so-called possible worlds semantics, a paradigm which is surveyed in this book, both as to its external sources of motivation and as to the internal dynamics of the resulting program. In particular, Manual of Intensional Logic presents the major classical (...) topics, including modal logic, tense logic, and conditional logic, all of which illustrate motivations coming from philosophy and linguistics. The Book also discusses recent computational applications in computer science and AI. Finally, Manual of Intensional Logic takes up recent developments in the study of language and information making themselves felt in the area. The Book examines the role of partial information--with illustrations drawn from different branches of Intensional Logic--and various influences stemming from current theories of the semantics of natural language, involving generalized quantifiers and theories of types. (shrink)

Retornando al modelo dialógico del discurso racional de la antigüedad, describimos a la lógica como el estudio del flujo general de la información: inferencia, observación y comunicación. Mostramos cómo esta perspectiva aúna ideas de la lógica estándar, la filosofía, la lingüística, la informática y la teoría de juegos.

Rapid developments in Artificial Intelligence are leading to an increasing human reliance on machine decision making. Even in collaborative efforts with Decision Support Systems (DSSs), where a human expert is expected to make the final decisions, it can be hard to keep the expert actively involved throughout the decision process. DSSs suggest their own solutions and thus invite passive decision making. To keep humans actively ‘on’ the decision-making loop and counter overreliance on machines, we propose a ‘reflection machine’ (RM). This (...) system asks users questions about their decision strategy and thereby prompts them to evaluate their own decisions critically. We discuss what forms RMs can take and present a proof-of-concept implementation of a RM that can produce feedback on users’ decisions in the medical and law domains. We show that the prototype requires very little domain knowledge to create reasonably intelligent critiquing questions. With this prototype, we demonstrate the technical feasibility to develop RMs and hope to pave the way for future research into their effectiveness and value. (shrink)

The European Clinical Trials Directive (EU 2001; 2001/20/EC) was introduced to improve the efficiency of commercial and academic clinical trials. Concerns have been raised by interested organizations and institutions regarding the potential for negative impact of the Directive on non-commercial European clinical research. Interested researchers within the European Group for Blood and Marrow Transplantation (EBMT) were surveyed to determine whether researcher experiences confirmed this view. Following a pilot study, an internet-based questionnaire was distributed to individuals in key research positions in (...) the European haemopoietic SCT community. Seventy-one usable questionnaires were returned from participants in different EU member states. The results indicate that the perceived impact of the European Clinical Trials Directive has been negative, at least in the research areas of interest to the EBMT. (shrink)

Aim: To examine how physicians’ life stances affect their attitudes to end-of-life decisions and their actual end-of-life decision-making.Methods: Practising physicians from various specialties involved in the care of dying patients in Belgium, Denmark, The Netherlands, Sweden, Switzerland and Australia received structured questionnaires on end-of-life care, which included questions about their life stance. Response rates ranged from 53% in Australia to 68% in Denmark. General attitudes, intended behaviour with respect to two hypothetical patients, and actual behaviour were compared between all large (...) life-stance groups in each country.Results: Only small differences in life stance were found in all countries in general attitudes and intended and actual behaviour with regard to various end-of-life decisions. However, with regard to the administration of drugs explicitly intended to hasten the patient’s death , physicians with specific religious affiliations had significantly less accepting attitudes, and less willingness to perform it, than non-religious physicians. They had also actually performed PAD less often. However, in most countries, both Catholics and Protestants reported ever having made such a decision.Discussion: The results suggest that religious teachings influence to some extent end-of-life decision-making, but are certainly not blankly accepted by physicians, especially when dealing with real patients and circumstances. Physicians seem to embrace religious belief in a non-imperative way, allowing adaptation to particular situations. (shrink)