Negational Fragment of Intuitionistic Control Logic
Anna Glenszczyk

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Logic, programming, and type systems
