Bücher der Reihe Trends in Logic

Goedel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Goedel argument is fully formalized.

'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation.

This book is for researchers in computer science, mathematical logic, and philosophical logic. It shows the state of the art in current investigations of process calculi with mainly two major paradigms at work: linear logic and modal logic.

This book presents adaptive logics (ALs) as an intuitive and powerful framework to model defeasible reasoning. It offers case studies stemming from various contexts of defeasible reasoning, such as default reasoning, argumentation, and normative reasoning.

Offering an expansive critical commentary, this meticulous assessment of the ground-breaking work of the philosopher Stanislaw Lesniewski focuses exclusively on primary texts and explores the full range of work by a master logician of the Lvov-Warsaw school.

The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997.

In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica.

This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic.

The Convergence of Scientific Knowledge-a view from the limit utilizes a few concepts from formal learning theory to study problems in modal logic and epistemology. It should be duely noted that this book has virtually nothing to do with formal learning theory or inductive learning problems.

This critical analysis of all the classic logical paradoxes, both ancient and modern, systematically surveys different approaches, introduces original solutions to many prominent paradoxes, and assesses the role played by paradoxes in philosophy and ontology.

This book is about proof theory for (the main systems of) modal logic. It is the first book to give a uniform and exhaustive presentation of both types of sequent calculus for modal logic, the purely syntactic sequent calculi as well as the semantic ones.

Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices, this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures.

Here is a thoroughly elaborated logical theory of generalized truth-values, presenting the idea of a trilattice of truth values - a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity.

Here is an extensive treatment of Natural Deduction and related proof systems, focused on practical aspects of proof methods. Necessary background material is provided, including a presentation of Modal Logics, First-Order Modal and Hybrid Modal Logics.

The Convergence of Scientific Knowledge-a view from the limit utilizes a few concepts from formal learning theory to study problems in modal logic and epistemology. It should be duely noted that this book has virtually nothing to do with formal learning theory or inductive learning problems.

This volume is easily accessible to young people and mathematicians unfamiliar with logic. It further provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The book is for trainees and professional model theorists, and mathematicians working in Algebra and Geometry.

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis.

This book proposes an original treatment of quantification, and it formulates insightful general principles of syntactic analysis. Its main message is that categorical grammar is the most plausible framework for logical syntax of natural language.

The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997.

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis.