Algebraic Perspectives on Substructural Logics

1. Front Matter

   Pages i-x

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2. Editorial Introduction

   • Davide Fazio, Antonio Ledda, Francesco Paoli

   Pages 1-9

3. Distributivity and Varlet Distributivity

   • Paolo Aglianò

   Pages 11-20

4. On Distributive Join Semilattices

   • Rodolfo C. Ertola-Biraben, Francesc Esteva, Lluís Godo

   Pages 21-40

5. Implication in Weakly and Dually Weakly Orthomodular Lattices

   • Ivan Chajda, Helmut Länger

   Pages 41-56

6. Residuated Operators and Dedekind–MacNeille Completion

   • Ivan Chajda, Helmut Länger, Jan Paseka

   Pages 57-72

7. PBZ\(^{*}\)–Lattices: Ordinal and Horizontal Sums

   • Roberto Giuntini, Claudia Mureşan, Francesco Paoli

   Pages 73-105

8. EMV-Algebras—Extended MV-Algebras

   • Anatolij Dvurečenskij, Omid Zahiri

   Pages 107-132

9. Quasi-Nelson; Or, Non-involutive Nelson Algebras

   • Umberto Rivieccio, Matthew Spinks

   Pages 133-168

10. Hyperdoctrines and the Ontology of Stratified Semantics

    • Shay Allen Logan

    Pages 169-193

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. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural logics are applicable to the mathematical investigation of such processes as resource-conscious reasoning, approximate reasoning, type-theoretical grammar, and other focal notions in computer science. They also apply to epistemology, economics, and linguistics. The recourse to algebraic methods-- or, better, the fecund interplay of algebra and proof theory -- has proved useful in providing a unifying framework for these investigations. The AsubL series of conferences, in particular, has played an important role in these developments.

This collection will appeal to students and researchers with an interest in substructural logics, abstract algebraic logic, residuated lattices, proof theory, universal algebra, and logical semantics.

• Substructural Logics
• Abstract Algebraic Logic
• Residuated Lattices
• Proof Theory
• Universal Algebra
• Logical Semantics
• Proof Theory of Substructural Logics
• Game-theoretic Semantics
• Algebraic Structures
• Investigation of Substructural Logics
• Abstract Algebraic Logic Duality
• Families of Logics
• Algebra and Substructural Logics
• Residuated Lattices Algebraic Structures

• Dipartimento di Pedagogia, Psicologia, Filosofia, Università di Cagliari, Via Is Mirrionis, Italy

  Davide Fazio, Antonio Ledda, Francesco Paoli

Davide Fazio is a Post-Doctoral Research Fellow at the University of Cagliari

Antonio Ledda is Full Professor of Logic at the University of Cagliari. His interests include algebraic logic, universal algebra, and the foundations of physics.

Francesco Paoli is a Full Professor of Logic  at the University of Cagliari. He published, among other things, the book Substructural Logics: A Primer (Kluwer, 2002) and over 50 papers in international peer-reviewed journals. His research interests include nonclassical (substructural, quantum, many-valued) logics, universal algebra, and the foundations of physics.

  

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