A proof system for fork algebras and its applications to reasoning in logics based on intuitionism

Marcelo F Frias, Ewa Orlowska


Relational proof systems have been already proposed for certain modal, relevant and substructural logics. In this paper we present a general method for constructing Rasiowa-Sikorski-style deduction systems for
nonclassical logics within the powerful relational framework of fork algebras. We apply the method to intuitionistic logic and a wide class of intermediate logics. The method consists in establishing interpretability of these logics in relational logics based on fork algebras (referred to as fork logics) and in developing a Rasiowa-Sikorski-like calculus for the respective fork logics. We prove soundness and completeness of the presented proof systems.

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