Bøger i Trends in Logic serien

Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.

States and proves various theorems of many-valued propositional logic. This text provides developments and trends, including applications to adaptive error-correcting binary search. It contains material, such as a simple proof of completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit.

Fuzzy logic in narrow sense is a promising new chapter of formal logic whose basic ideas were formulated by Lotfi Zadeh (see Zadeh [1975]a). By contrast, fuzzy logical deductive machinery is devised to produce a fuzzy set of formulas (the theorems) from a fuzzy set of formulas (the hypotheses).

Proof theory and category theory were first drawn together by Lambek some 30 years ago but, until now, the most fundamental notions of category theory (as opposed to their embodiments in logic) have not been explained systematically in terms of proof theory.

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.

"Is quantum logic really logic?" The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking. from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation.

'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.

The approach to probability theory followed in this book (which differs radically from the usual one, based on a measure-theoretic framework) characterizes probability as a linear operator rather than as a measure, and is based on the concept of coherence, which can be framed in the most general view of conditional probability.

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.

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.

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.

'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.

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.

Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs).

Develops a hybrid architecture that allows to incorporate anaphora resolution into grammatical deduction. After giving an introduction into Type Logical Grammar in general, this book discusses the formal properties of this connective.

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.

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.

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.

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.

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.

This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics.

a

"Is quantum logic really logic?" The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking. from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation.

This book discusses the theory of triangular norms and surveys several applied fields in which triangular norms play a significant part: probabilistic metric spaces, aggregation operators, many-valued logics, fuzzy logics, sets and control, and non-additive measures together with their corresponding integrals.