Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.

Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

Other Logics: Alternatives to Formal Logic in the History of Thought and Contemporary Philosophy challenges the widespread idea of formal logic as inherently monolithic, universal, and ahistorical. Written by both leading and up-and-coming scholars, and edited by Admir Skodo, Other Logics offers a wide variety of historical and philosophical alternatives to this idea, all arguing that logic is a historical, concrete, and multi-dimensional phenomenon. To name a few examples, Frank Ankersmit lays down a representationalist logic, Alessandra Tanesini forcefully argues for the possibility of logical aliens, Christopher Watkin analyzes how leading contemporary French philosophers view the idea of logic, and Aaron Wendland unearths Heidegger's critique of formal logic. In Other Logics readers will find provocative interventions in a highly contested field in contemporary philosophy. Contributors include: Frank Ankersmit, Christopher Watkin, Giuseppina D'Oro, Alessandra Tanesini, Admir Skodo, Aaron Wendland, Ervik Cejvan, Anders Kraal, Christopher Fear, Karim Dharamsi, Johan Modée, and Thord Svensson.

In the last century, developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This book embodies the multi-dimensional interplay between logic and science, presenting contributions from the world's leading scholars on new trends and possible developments for research.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers. Part I provides an introduction to the subject as a whole, as well as to the basic theory and examples. The rest of the book addresses finitary languages with additional quantifiers, infinitary languages, second-order logic, logics of topology and analysis, and advanced topics in abstract model theory. Many chapters can be read independently.

The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only to establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics.

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected here address the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. The monograph provides a succinct picture of recent research in alternative logics as they have been developed for applications in the sciences.

This study introduces some central ideas and lines of research in finite model theory - particularly bounded variable infinitary logics - and explores the fruitful exchange between ideas from logic and from complexity theory that is characteristic of finite model theory.

This book constitutes the refereed proceedings of the European Conference on Logics in Artificial Intelligence, JELIA 2002, held in Cosenza, Italy in September 2002.The 41 revised full papers presented together with 11 system descriptions and 3 invited contributions were carefuly reviewed and selected from more than 100 submissions. The papers are organized in topical sections on multi-agent systems, evolution and changes, description logic and the semantic web, complexity issues, probabilistic logic, AI planning, modal logic and causal reasoning, theory, reasoning under uncertainty, satisfiability, paraconsisten reasoning, actions and caution, logic for agents, semantics, and optimization issues in answer set semantics.