This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combinatorial methods to obtain results in proof theory, such as incompleteness theorems or a description of the provably total functions of a theory.
In the first chapter, the authors first discusses ordinal combinatorics of finite sets in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems of Peano Arithmetic as well as for combinatorial independence results. Next, the volume examines a variety of proofs...
This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combi...
This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics.
Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions....
This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Alg...
This volume clusters together issues centered upon the variety of types of intensional semantics. Consisting of 10 contributions, the volume is based on papers presented at the Trends in Logic 2019 conference. The various chapters introduce readers to the topic, or apply new types of logical semantics to elucidate subtleties of logical systems and natural language semantics.
The book introduces hyperintentional systems that aim at solving some open philosophical problems. Specifically, the first three studies focus on relating semantics, while the following ones...
This volume clusters together issues centered upon the variety of types of intensional semantics. Consisting of 10 contributions, the volume is b...
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. 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. It includes the basics of the...
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties an...
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. 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. It includes the basics of the...
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties an...
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...
This book is the first to present a comprehensive investigation of the technical features of the metainferential logics developed in the last ...
