Multi-Dimensional Modal Logic

Multi-Dimensional Modal Logic by Maarten Marx, Yde Venema.

Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our defini...

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Bibliographic Details
Main Authors: Marx, Maarten (Author), Venema, Yde (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 1997.
Edition:1st ed. 1997.
Series:Applied Logic Series, 4
Springer eBook Collection.
Subjects:
Logic.
Mathematical logic.
Computational linguistics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Multi-dimensional modal logic
  • 1.1 What is multi-dimensional modal logic?
  • 1.2 Manifestations of multi-dimensional modal logics
  • 1.3 Themes and questions
  • 1.4 Overview of the book
  • 1.5 How to read this book
  • 2 Two-dimensional modal logics
  • 2.1 Operations on the square universe
  • 2.2 Axiomatizing S5-square
  • 2.3 Cylindric modal logic of squares
  • 2.4 The modal logic of composition
  • 2.5 A two-dimensional temporal logic
  • 2.6 Historical notes
  • 3 Arrow logic
  • 3.1 Introduction
  • 3.2 Motivation
  • 3.3 Arrow logic and relation algebras
  • 3.4 Connection with first order logic
  • 3.5 Characterizing (local) squares
  • 3.6 Axiomatizing (local) squares
  • 3.7 Decidability and interpolation
  • 3.8 Temporal arrow logic
  • 3.9 Other directions in arrow logic
  • 4 Modal logics of intervals
  • 4.1 Introduction
  • 4.2 The System HS: Introduction
  • 4.3 The system HS: expressiveness
  • 4.4 The System HS: Axiomatics
  • 5 Modal logics of relations
  • 5.1 Introduction
  • 5.2 Modalizing first-order logic
  • 5.3 Abstract and generalized assignment frames
  • 5.4 Characterizing cubes and local cubes
  • 5.5 Meta-properties
  • 5.6 Infinite dimensions
  • 5.7 Connections
  • 6 Multi-dimensional semantics for every modal language
  • 6.1 Logics with one modality
  • 6.2 Logics with arbitrary many modalities
  • 6.3 Versatile similarity types
  • 6.4 The modal logic of composition and its conjugates
  • Open problems
  • Appendices
  • A Modal Similarity Types
  • A.1 Introduction
  • A.2 Modal similarity types
  • A.3 Frames, models and correspondence
  • A.4 Structural frame operations
  • A.5 Boolean S-algebras
  • A.6 Frames and algebras
  • A.7 Modal logics and derivation systems
  • A.8 Algebraic derivations
  • A.9 Canonical structures
  • B A Modal Toolkit
  • B.1 Sahlqvist theory
  • B.1.1 Definitions
  • B.1.2 Sahlqvist correspondence
  • B.1.3 Canonicity & completeness
  • B.1.4 Algebraic aspects of Sahlqvist theory
  • B.2 Logical operators
  • B.2.1 The universal modality
  • B.2.2 Versatile similarity types
  • B.2.3 The D-operator
  • B.3 Negative definability and unorthodox axiomatics
  • B.4 Interpolation
  • B.5 Filtrations
  • B.6 A local and a global paradigm
  • List of symbols.

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