Heinrich Wansing Livres

Focusing on proof systems for modal and constructive logics, this monograph delves into display logic, a refinement of Gentzen's sequent calculus. It highlights the rapid development of non-classical logics and aims to compare various generalized Gentzen systems, discussing their advantages and disadvantages. While not exhaustive, the work builds on previous research and provides introductory context in each chapter. The author reflects on the philosophical implications and acknowledges contributions from various sources throughout the text.

This book explores a comprehensive logical theory of generalized truth-values, focusing on subsets of basic truth values. It discusses the significance of truth values in logic and philosophy, introduces four-valued logic and bilattices, and develops multilattices and trilattices, detailing their unique logical structures and relations.

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. The authors cover themes such as the knowability paradox, tableaux and sequent calculi, natural deduction, definite descriptions, identity, truth, dialetheism and possible worlds semantics. The developments presented here focus on challenging problems in the specification of fundamental philosophical notions, as well as presenting new techniques and tools, thereby contributing to the development of the field. Each chapter contains a bibliography, to assist the reader in making connections in the specific areas covered. Thus this work provides both a starting point for further investigations into philosophical logic and an update on advances, techniques and applications in a dynamic field. The chapters originate from papers presented during the Trends in Logic XI conference at the Ruhr University Bochum, June 2012.

Frontmatter -- PART I: NEGATION IN PHILOSOPHICAL LOGIC -- Generalized Ortho Negation / DUNN, J. MICHAEL -- Order-Duality, Negation and Lattice Representation / HARTONAS, CHRYSAFIS -- Necessary Conditions for Negation Operators / LENZEN, WOLFGANG -- External, Restricted External, and Internal Negations in a Two-Dimensional Logic / MAX, INGOLF -- Negation and Relevance / STELZNER, WERNER -- PART II: NEGATION IN LINGUISTICS -- Categorial Grammars with Negative Information / BUSZKOWSKI, WOJCIECH -- Negative Concord and ‘Mode of Judgement’ / LADUSAW, WILLIAM A. -- Litotes and Downward Monotonicity / WOUDEN VAN DER, TON -- A Hierarchy of Negative Expressions / ZWARTS, FRANS -- PART III: NEGATION IN ARTIFICIAL INTELLIGENCE -- The Role of Negation in Nonmonotonic Logic and Defeasible Reasoning / SCHURZ, GERHARD -- Belnap’s Epistemic States and Negation-as-Failure / WAGNER, GERD -- Index -- Backmatter

This volume honors Prof. Dag Prawitz for his significant contributions to philosophical and mathematical logic, particularly in structural proof theory and inference-based meaning theories. His work has greatly influenced modern proof theory and anti-realistic semantics. Prawitz is recognized as a key figure in natural deduction, alongside Gerhard Gentzen, who initially defined the concept in 1934. The book begins with an introductory paper that surveys Prawitz's extensive contributions, situating his work within a broader historical and systematic context. Subsequent chapters delve into specific aspects of Prawitz's research or explore open research problems related to core issues in structural proof theory. These range from philosophical essays to mathematical papers, addressing topics such as the necessity of thought, the theory of grounds, and computational justifications. The validity of inferences is examined through the lens of three "dogmas of proof-theoretic semantics." More formal discussions cover the constructive behavior of classical logic fragments and the modal logic S4, along with inversion principles, normalization of proofs, and proof-theoretic harmony. Prawitz also contributes a chapter outlining his views on the epistemic dimension of proofs, particularly why certain inferences effectively confer evidence on their conclusions when applied to premises already supported by evidence.