Negational Fragment of Intuitionistic Control Logic

TL;DR

This paper explores the properties of a negational fragment of Intuitionistic Control Logic, focusing on the relations between negational formulas and their structural organization.

Contribution

It introduces a monadic negational fragment of ICL with two falsum constants and analyzes the implicational relations and structure of negational formulas.

Findings

Identifies the poset structure of negational formulas

Defines two forms of negation based on different falsum constants

Analyzes implicational relations between negational formulas

Abstract

We investigate properties of monadic purely negational fragment of Intuitionistic Control Logic (ICL). This logic arises from Intuitionistic Propositional Logic (IPL) by extending language of IPL by additional new constant for falsum. Having two different falsum constants enables to define two forms of negation. We analyse implicational relations between negational monadic formulae and present a poset of non equivalent formulae of this fragment of ICL.