Algebraization of Non-Classical Logics

The following sections are included:

• Basic Definitions and Properties

• The Fork Logic FL

• Modal Logics

• Representation of Constraints in FL

• Interpretability of Modal Logics in FL

• A Proof Theoretical Approach

• Interpretability of Propositional Dynamic Logic in FL

• The Fork Logic FL′

  • Syntax of FL

  • Semantics of FL′

• A Rasiowa–Sikorski Calculus for FL′

  • The Deduction System for FL′

  • Soundness and Completeness of the Calculus FLC

  • Examples of Proofs in the Calculus FLC

• A Relational Proof System for Intuitionistic Logic

  • Intuitionistic Logic

  • Interpretability of Intuitionistic Logic in FL′

  • A Fork Logic Calculus for Intuitionistic Logic

    • Example

• A Relational Proof System for Minimal Intuitionistic Logic

• Relational Reasoning in Intermediate Logics

  • Method 1

  • Method 2

  • Method 3