Starting with the analysis of cognitive situations which appear in everyday life, and by means of the logical analysis of some games, the author deals with applied logic in the sense of the general methodology of reasoning. The book acquaints the reader with some forms and operations of reasoning which are applied in the process of scientific cognition as well as in daily activities that require thought. As opposed to a number of well-known and unique handbooks and text-books on pure logic this books conveys learning, and in many cases original thoughts, through witty dialogues, in an entertaining way.

What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the first half of the book he examines some key ideas in the historical development of the logic of entailment, looking in particular at the notion 'is derivable from' and at how symbolic logic has attempted to capture this notion. In the second half of the book he develops his own theory connecting ideas from the traditions in mathematical logic with some ideas in the philosophy of science. The book's fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.

What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon. This picture (explored more by decision-theorists and philosophers of science thatn by mainstream epistemologists) invites the use of probabilistic coherence to constrain rational belief. But this latter project has often involved defining graded beliefs in terms of preferences, which may seem to change the subject away from epistemic rationality. Putting Logic in its Place explores the relations between these two ways of seeing beliefs. It argues that the binary conception, although it fits nicely with much of our commonsense thought and talk about belief, cannot in the end support the traditional deductive constraints on rational belief. Binary beliefs that obeyed these constraints could not answer to anything like our intuitive notion of epistemic rationality, and would end up having to be divorced from central aspects of our cognitive, practical, and emotional lives. But this does not mean that logic plays no role in rationality. Probabilistic coherence should be viewed as using standard logic to constrain rational graded belief. This probabilistic constraint helps explain the appeal of the traditional deductive constraints, and even underlies the force of rationally persuasive deductive arguments. Graded belief cannot be defined in terms of preferences. But probabilistic coherence may be defended without positing definitional connections between beliefs and preferences. Like the traditional deductive constraints, coherence is a logical ideal that humans cannot fully attain. Nevertheless, it furnishes a compelling way of understanding a key dimension of epistemic rationality.

This book traces the development of Dialectical Logic within the history of modern western philosophy, culminating in Marx s materialist dialectics. It brings out the essential contours of Logic through a detailed exposition of the ontological and epistem

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 4th Indian Conference on Logic and Its Applications, ICLA 2011, held in Delhi, India, in January 2011. The 14 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 34 submissions. The papers present current research in all aspects of formal logic ranging from pure and applied logic to history of logic.

This book offers a multifaceted perspective on fuzzy set theory, discussing its developments over the last 50 years. It reports on all types of fuzzy sets, from ordinary to hesitant fuzzy sets, with each one explained by its own developers, authoritative scientists well known for their previous works. Highlighting recent theorems and proofs, the book also explores how fuzzy set theory has come to be extensively used in almost all branches of science, including the health sciences, decision science, earth science and the social sciences alike. It presents a wealth of real-world sample applications, from routing problem to robotics, and from agriculture to engineering. By offering a comprehensive, timely and detailed portrait of the field, the book represents an excellent reference guide for researchers, lecturers and postgraduate students pursuing research on new fuzzy set extensions.

This volume contains the proceedings of the Eighth International Workshop on Rewriting Logic and its Applications (WRLA 2010) that was held in Paphos, Cyprus, March 20–21, 2010, as a satellite workshop of the European Joint C- ferences on Theory and Practice of Software (ETAPS 2010). Rewriting logic is a natural semantic framework for representing conc- rency,parallelism,communicationandinteraction,aswellasbeing anexpressive (meta)logical framework for representing logics. It can then be used for spe- fying a wide range of systems and programming languages in various appli- tion ?elds. In recent years, several executable speci?cation languages based on rewriting logic (ASF+SDF, CafeOBJ, ELAN, Maude) have been designed and implemented. The aim of the WRLA workshop series is to bring together - searchers with a common interest in rewriting logic and its applications, and to give them the opportunity to present their recent works, discuss future research directions, and exchange ideas. Previous WRLA workshops were held in Asilomar (1996), Pont-a-Mousson ` (1998), Kanazawa (2000), Pisa (2002), Barcelona (2004), Vienna (2006), and Budapest (2008), and their proceedings have been published inElectronic Notes in Theoretical Computer Science. In addition, selected papers from WRLA 1996 have been published in a special issue of Theoretical Computer Science,and selected papers from WRLA 2004 appeared in a special issue of Higher-Order and Symbolic Computation.

The unicist logic provided the necessary logical structure to approach complex and chaotic realities. It provided a logical integration for the preexisting logical models. Logical formalizations are born to sustain ideas, consolidate knowledge or solve problems. Unicist Logic's main added value is the provision of a logical structure to analyze reality and complex problems as a unified field. Unicist logic makes the integration of possibilities and probabilities "possible." It provided the logical groundings for the Unicist Ontology of Evolution. Its mathematics provides the tools to define the probabilities of the evolution when the "true" facts of reality are known. The logical relations between the purpose, the active principle and the energy conservation principle that underlie reality are defined as formal logical structures that can be found, measured, and solved mathematically to provide operational solutions to approach complex realities. This work includes the groundings of the unicist ontology to research the nature of evolution.