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Interest in the age-old problems of universals and individuation has received a new impetus from the current revival of ontology in the analytic tradition, the development of theories of individual properties (and the related application of mereological calculi to the analysis of predication), and the particular problems posed by relational predication and the nature of particulars. The essays explore aspects of the history of the issues and attempt to deal with the issues and with challenges to the distinctions that give rise to them. They continue the debates stemming from the revival of metaphysics rooted in Freges realism, the Austrian tradition of Brentano-Husserl-Meinong, and the early 20th century revolt against idealism embodied in writings of Moore and Russell and culminating in Wittgensteins Tractatus.
In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
A Mathematical Introduction to Logic
Computation, itself a form of calculation, incorporates steps that include arithmetical and non-arithmetical (logical) steps following a specific set of rules (an algorithm). This uniquely accessible textbook introduces students using a very distinctive approach, quite rapidly leading them into essential topics with sufficient depth, yet in a highly intuitive manner. From core elements like sets, types, Venn diagrams and logic, to patterns of reasoning, calculus, recursion and expression trees, the book spans the breadth of key concepts and methods that will enable students to readily progress with their studies in Computer Science.
Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.
Covers research in complex predicates within a variety of languages, such as German, Dutch, Italian, French, Korean and Urdu. This work focuses on diverse aspects of complex predicate phenomena, including order variation, constituency relations, interactions with other construction types, argument relations, and the syntax morphology interface.
This book deals with atypical predicate-argument relations. Although the relations between predicates, especially verbal, and their arguments have been long studied, most studies are concerned with typical telic verbs in the past tense, indicative mood, active voice, with all arguments expressed. Recently, linguists have become interested in other types of predicate-argument relations displaying atypical properties, be they morphological or syntactic, in one language or cross-linguistically. The articles in this book investigate some of these: argument marking with some special groups of verbs, arguments not foreseen in the verb valency and contributed by the construction, verbs in idiomatic constructions, valency-changing operations, arguments in thetic sentences or in participle constructions etc. The authors work within different theoretical frameworks and on various languages, from more current languages like English, Spanish, French or German, to Hebrew or lamaholot, an Austronesian language.
Complex predicates can be loosely defined as a sequence of items that behave as a single predicate, projecting a single argument structure within a clause. Each of the members of the predicate contributes part of the information ordinarily associated with a single head. The present volume presents a collection of theoretical linguistic results on the study of complex predicates in different perspectives and with a variety of approaches. Important empirical and theoretical issues cutting across various subfields of linguistics are being addressed in this book, such as: • Syntactic and semantic modeling of complex predicate formation: compositionality, argument structure, event structure. • Differences between syntactic and morphological processes of lexeme formation. • Typological and diachronic issues in complex predicate formation. • Neo-Davidsonian analyses of abstract predicate decomposition and its morphological correlates. Contributors are: Ane Berro, Denis Creissels, Hannah Gibson, Adele Goldberg, Lutz Marten, Annie Montaut, Léa Nash, Pooja Paul, Pollet Samvelian, Peter Svenonius, and Susanne Wurmbrand.