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An Easy Road to Multi-contra-classicality.

Luis Estrada-González^1,2

¹Institute for Philosophical Research, UNAM, Mexico City, Mexico.

|October 25, 2021

Summary

This summary is machine-generated.

This study explores contra-classical logics, demonstrating that Mortensen's three-valued connexive logic (M3V) exhibits key features. Further development can yield logics with even more contra-classical properties.

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Area of Science:

* Mathematical Logic
* Philosophy of Logic

Background:

* Classical logic provides a standard framework for valid arguments.
* Contra-classical logics validate arguments not accepted in classical logic.
* Existing contra-classical logics present diverse features.

Purpose of the Study:

* To identify a single, non-trivial logic with multiple contra-classical features.
* To investigate the potential for unifying characteristics of known contra-classical logics.
* To explore methods for constructing logics with enhanced contra-classical properties.

Main Methods:

* Analysis of Mortensen's three-valued connexive logic (M3V).
* Construction of new logics by combining a suitable conditional with the LP-fragment.
* Comparative study of logical validity across classical and contra-classical systems.

Main Results:

* Mortensen's three-valued connexive logic (M3V) is identified as a logic exhibiting numerous contra-classical features.
* A method for constructing logics with expanded contra-classical characteristics is demonstrated.
* The proposed approach allows for the creation of logics with more contra-classical properties than M3V.

Conclusions:

* Mortensen's three-valued connexive logic (M3V) serves as a significant example of a unified contra-classical logic.
* The methodology of combining conditionals with the LP-fragment offers a pathway to novel contra-classical logics.
* Further research can explore the full spectrum of contra-classical features achievable through this construction.