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This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos.

This book is the first to present a comprehensive investigation of the technical features of the metainferential logics developed in the last years, with their most relevant results and applications. It provides some new paths to define and investigate metainferential logics and offers a thorough study of the semantics and the proof-theories of this new and exciting variety of families of logics.This volume examines the hierarchies of metainferential logics and gives a general and systematic theory of them, and of the truth theories based on these logics. This book puts forward the prospects for truth-theories based on the metainferential logics of the TS/ST hierarchy and argues for its promise noting that each of these logics can be safely expanded with a transparent truth predicate. It also goes onto to explore new developments in three fields related to logics ¿ namely metainferential logics built by means of the Weak Kleene schema and combining them with logics defined through the Strong Kleene schema, proof-theoretic presentations, and those with a with a global or an absolutely global validity standard, instead of a local one. This book is of interest to scholars in formal logic.

By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties.The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos.

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics.

This volume clusters together issues centered upon the variety of types of intensional semantics.

This volume presents the state of the art in the algebraic investigation into substructural logics.

This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results.

This volume clusters together issues centered upon the variety of types of intensional semantics.

This volume presents the state of the art in the algebraic investigation into substructural logics.

This book presents an English translation of a classic Russian text on duality theoryfor Heyting algebras.

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 purpose of this book is to present unpublished papers at the cutting edge of research on dialetheism and to reflect recent work on the applications of the theory. It includes contributions from some of the most respected scholars in the field, as well as from young, up-and-coming philosophers working on dialetheism.Moving from the fringes of philosophy to become a main player in debates concerning truth and the logical paradoxes, dialetheism has thrived since the publication of Graham Priest¿s In Contradiction, and several of the papers find their roots in a conference on dialetheism held in Glasgow to mark the 25th anniversary of Priest¿s book. The content presented here demonstrates the considerable body of work produced in this field in recent years.With a broad focus, this book also addresses the applications of dialetheism outside the more familiar area of the logical paradoxes, and includes pieces discussing the application of dialetheism in metaphysics, philosophy of language, and philosophy of mind.

Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion.

This book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives, they shed a new light on the question of whether paraconsistent logics can function as the underlying logics of inconsistent but useful scientific and mathematical theories. The great variety of paraconsistent logics gives rise to various, interrelated questions, such as what are the desiderata a paraconsistent logic should satisfy, is there prospect of a universal approach to paraconsistent reasoning with axiomatic theories, and to what extent is reasoning about sets structurally analogous to reasoning about truth. Furthermore, the authors consider paraconsistent logic's status as either a normative or descriptive discipline (or one which falls in between) and which inconsistent but non-trivial axiomatic theories are well understood by which types of paraconsistent approaches. This volume addresses such questions from different perspectives in order to (i) obtain a representative overview of the state of the art in the philosophical debate on paraconsistency, (ii) come up with fresh ideas for the future of paraconsistency, and most importantly (iii) provide paraconsistent logic with a stronger philosophical foundation, taking into account the developments within the different schools of paraconsistency.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic.

Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion.

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory.The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked toprovide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory.The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

Toward Predicate Approaches to Modality

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. 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.

Advances in Natural Deduction

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.