LJ calculus with stoup: A pedagogical approach

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We prove a theorem in calculus LJ and in LJT (LJ with stoup) as well. We show that while there are many proofs to one single theorem in LJ, there is exactly one proof in LJT.

https://doi.org/10.31219/osf.io/z6h4q

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 268, 2022 [KN]

The logic of entanglement in gravity

[microresearch]

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We explore the relation between gravity and entanglement using mathematical logic (Modus Ponens).

https://doi.org/10.31219/osf.io/m2dca

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 58, 2019 [CF]

Hilbert-style proof Calculus for Propositional Logic in ABC notation

[microreview]

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All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

https://doi.org/10.31219/osf.io/jd3gp

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 57, 2019 [CE]

The Incorrectness Lemma

[original idea]

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We address two questions. Is there an Incorrectness Lemma? Is this system complete?

https://doi.org/10.31219/osf.io/f8p7k

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 53, 2019 [CA]

A pedagogical approach to convert “if and only if” to “if then”

[microreview]

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We show, using the equivalence of some formulas, that (A iff B) ~ ((A v B) => (A ^ B)).

https://doi.org/10.31219/osf.io/xhzc9

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 52, 2019 [BZ]

Generalized Pierce law

[microresearch]

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An extension of the Pierce law is presented, considering n “if then” connectives.

https://doi.org/10.31219/osf.io/6fbgp

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 50, 2019 [BX]