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Connexive Exclusion.

Yaroslav Shramko¹, Heinrich Wansing²

¹Department of Philosophy, Kryvyi Rih State Pedagogical University, Kryvyi Rih, 50086 Ukraine.

Erkenntnis

|December 22, 2025

Summary

This study introduces connexive exclusion logic, defining principles for this propositional connective dual to implication. The research develops a semantic approach, resulting in a contradictory yet non-trivial logic system.

Area of Science:

Formal Logic
Mathematical Logic
Philosophy of Logic

Background:

Exclusion, also known as co-implication, is a propositional connective.
It is considered dual to the connective of implication.
Exclusion is non-connexive in classical and intuitionistic logics, failing to meet connexivity principles.

Purpose of the Study:

To present a logic dealing with connexive exclusion.
To formulate principles for connexive exclusion, dual to Aristotle's and Boethius' theses for implication.
To develop a semantic approach for a logic of connexive exclusion.

Main Methods:

Formulating principles for connexive exclusion.
Defining criteria for a logical system to be considered a logic of connexive exclusion.

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Developing a semantic justification for the exclusion connective.

Using connexive logic C as a paradigm.

Main Results:

Exclusion is non-connexive in standard logics.
Principles for connexive exclusion are formulated.
A logic of connexive exclusion is proposed, requiring asymmetry of the exclusion connective.
The developed logic is shown to be contradictory but not trivial.

Conclusions:

Connexive exclusion logic can be formally defined with specific principles.
A semantic approach provides a foundation for this logic.
The resulting logic, while contradictory, offers a non-trivial system for studying exclusion.