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**Jesper Agdakx** @jesper@agda.club · 7 avr. *

With the NWO XL consortium on Cyclic Structures in Programs and Proofs, we are looking for 6 highly motivated and talented PhD students starting in September (with some flexibility).

The topics range from Modal logic, proof theory, and coalgebras to Programming languages, concurrency, and type systems and Proof assistants (#Agda, #Rocq).

Information about the positions and application procedure can be found on the website:

cyclic-structures.gitlab.io/vacancies/

Applications will be evaluated on a rolling basis but should be submitted by the 23rd of May for full consideration.

Please forward to any strong candidates you know!

#TypeTheory #ModalLogic #Concurrency #ProgrammingLanguages #TypeSystems #ProofAssistants #CyclicStructures #PhD #Netherlands #UniversityOfGroningen #LeidenUniversity #UniversityOfTwente #TUDelft #RadboudUniversity

Cyclic Structures in Programs and ProofsVacanciesPar Jorge Perez

#radbouduniversity

**Greg Restall** @consequently@hcommons.social · 20 janv.

20 janv.

Greg Restall @consequently@hcommons.social

I'm glad to have space to get to writing, and the first writing project of my sabbatical has reached first-draft stage. If you're interested in modal logic, proof theory, and the metaphysics of contingent existence, have I got the paper for you!

https://consequently.org/writing/mlce-ge2/

I've got to say, I think the hypersequent calculus in this paper is pretty neat.

Structural rules, term rules and defining rules in a hypersequent calculus for a first-order modal logic.

#ProofTheory #ModalLogic #Metaphysics

**Greg Restall** @consequently@hcommons.social · 10 juin 2024

10 juin 2024

Greg Restall @consequently@hcommons.social

The Nordic Logic Summer School is now in full swing here in Reykjavík. I’ve given my first proof theory class, and Rineke Verbrugge is introducing modal logic and social cognition.

https://consequently.org/class/2024/nls-proof-theory/

Rineke Verbrugge introducing her class on modal logic and social cognition. She stands in front of a slide, containing the text:

Overview rest of the talk:

• 1. The first- & second-order false belief task
— Computational cognitive models of 5 year old children who are on the brink of developing second-order ToM

• Il. The Colored Trails game
— Using a software agent to entice students' theory of mind

• III The Marble Drop game
— What makes applying second-order ToM in a turn-taking game so difficult?

#ProofTheory #ModalLogic

**Samiro Discher** @xamidi@mastodon.social · 9 avr. 2024

9 avr. 2024

Samiro Discher @xamidi@mastodon.social

An explanation of what axioms and mathematical proofs really are. With a reference to my tool that helps exploring some of them.

https://math.codidact.com/posts/290943/291261#answer-291261

math.codidact.comWhat is the significance of the K-axiom in modal logic S5?In normal modal logic S5, the K axiom says $\square (p \rightarrow q) \rightarrow (\square p \rightarrow \square q)$. First of all, is this an abuse...

#Logic #Axioms #Mathematics

**Robbie Norlyn, Author** @robertnorlyn@mstdn.social · 9 juil. 2023

9 juil. 2023

Robbie Norlyn, Author @robertnorlyn@mstdn.social

Did you know that some people will refuse a slice of cake if you don’t give them a chance to eat the whole cake?
Also, did you know that there is no point in driving anywhere if you can’t travel at the speed of light?
#ModalLogic #Capitalism #IncomeCap

**Greg Restall** @consequently@scholar.social · 1 déc. 2022 *

1 déc. 2022 *

Greg Restall @consequently@scholar.social

Let’s ask ChatGPT the truly serious questions, starting off with some quantified modal logic and the necessitism/contingentism debate.

(Unsurprisingly, it sounds like an undergraduate who has some sense of what the words mean but hasn't done the work and is doing a bad job of word association and looking up Wikipedia summaries.)

A ChatGPT transcript.

I ask: “Suppose it is possible that there is something that is F. Does it follow that there is something such that it is possibly F?”

ChatGPT responds: Yes, if it is possible that there is something that is F, then it follows that there is something such that it is possibly F. This is because "it is possible that there is something that is F" is equivalent to "there is something that is possibly F", and "there is something that is possibly F" is logically equivalent to "there is something such that it is possibly F". These statements are logically equivalent because they have the same truth conditions: they are both true when there exists at least one thing that is F, and they are both false when there does not exist any thing that is F. Therefore, if it is possible that there is something that is F, then it follows that there is something such that it is possibly F.

Continuing I say:

I don't understand this. Could you please explain why "it is possible that there is something that is F" is equivalent to "there is something that is possibly F". | think you've ignored the difference in scopes of the quantifiers in the two expressions.

ChatGPT responds: You are correct that there is a difference in the scope of the quantifiers in the two expressions. In the first expression, "it is possible that there is something that is F", the quantifier "there is" applies to the entire statement "something that is F", whereas in the second expression, "there is something that is possibly F", the quantifier "there is" only applies to the subject "something". However, this difference in the scope of the quantifiers does not affect the logical equivalence of the two expressions.

To see why, consider the following argument:

1. ltis possible that there is something that is F.

2. Therefore, there exists at least one thing x such that it is possible that x is F.

3. Therefore, there is something that is possibly F. In this argument, we start by assuming the first expression (line 1), which implies that there exists at least one thing x such that it is possible that x is F (line 2). We can then conclude that there is something that is possibly F (line 3) by applying the quantifier "there is" to the subject "something". This shows that the two expressions are logically equivalent, despite the difference in the scope of their quantifiers.

A further ChatGPT transcript, wherein I give a putative counterexample to the Barcan inference from "it's possible that something is F" to "something is possibly F" and ChatGPT gives a confused and confusing response.

#PhilLogic #ModalLogic #ChatGPT

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