axiom | dynamic infrastructure framework for everybody | Security library

Say we have a proposition P1 n, and there exists n for which it holds. Furthermore we have a proposition P2, where P1 n implies P2 for any n. How do we prove P2?

I am trying to call an OWL API java program through terminal and it crashes, while the exact same code is running ok when I run it in IntelliJ.

The exception that rises in my main code is this:

I want to programmatically get explanations for inferred axioms in consistent ontologies, in a similar manner that one can do in the Protégé UI. I cannot find any straightforward way. I have found the owlexplanation repo, but I cannot for the life of me solve the dependency issues to set up the owlexplanation environment. I have also browsed the javadoc of owlapi regarding explanations (to avoid the other repo altogether), but I don't see anything useful beyond what I can already see browsing the Java source code.

I have thought of simply negating the inferred axiom, to get explanations through inconsistencies, but I would prefer something cleaner, and I am not sure this approach is correct anyway.

Other (possibly) useful context:

• I had used some Java years ago, but I now primarily use Python (I try to use OWL API with JPype and OWL in general with Owlready2).
• I am using HermiT reasoner (again through JPype) (according to build.xml file, latest stable version 1.3.8).
• I have managed to get explanations for unsatisfiability and inconsistency in my setup, without owlexplanation, following this example from the HermiT source code.
• I fell in the rabbit hole wanting to make a usable .jar file for owlexplanation, in order to add it in my JPype classpath. My plan went sideways when I couldn't get the Java project to build in the first place.
• I am using Intellij IDE.

I would appreciate any insight or tips.

UPDATE Jan 6, 2022:

I decided to try once more with the owlexplanation code with a clean head so here is where I am at:

• Downloaded the source code from github and extracted the zip.
• Started IntelliJ and instead from "Creating a project from Existing sources", I clicked "Open" and selected the extracted directory.
• I built the project and it did successfully.
• From Maven tools, I run clean, validate, compile and test succesfully.
• If I run "package" Maven action, it throws as error that "The environment variable JAVA_HOME is not correctly set". The thing is that if I go File>Project Structure, I see that SDK is set to 11, it's not empty.
• Additionally, from the pom.xml file I get these problems:
  • Plugin 'org.apache.maven.plugins:maven-gpg-plugin:1.5' not found
  • Plugin 'org.sonatype.plugins:nexus-staging-maven-plugin:1.6.6' not found

UPDATE Jan 8, 2022: (Trying @Ignazio's answer)

I created a new IntelliJ project, and added the Maven dependencies @Ignazio mentioned (plus some others like slf4j etc) and I got a working example (I think). Moving to my main project (using JPype), I had to manually download some .jars to include in the classpath (as maven can't be used here). These are the ones downloaded so far:

UIP (and equivalents like axiom K) must be added axiomatically in Coq if it is desired:

I'm learning to use Coq and I try to prove the theorems of a paper I'm reading. The paper is Having a Part Twice Over of Karen Bennett, published in 2013. The paper propopes a mereological theory composed of two primitives F and Ps and defines the parthood relation P using the two primitives.

I coded it as follows:

I try to implement on Alloy the axiomatic system described in a paper on mereology: "Bennett, Having a Part Twice Over, 2013".

I implemented all the axioms, and I thought that if I implemented them correctly, I could assert and check the theorems.

I try to code theorem (T9). This is the theorem in the paper:

And this is how I coded it:

I am trying to upgrade tailwind to version 3 in my Laravel application.

I followed the installation as instructed in

https://tailwindcss.com/docs/upgrade-guide#upgrade-packages

npm install -D tailwindcss@latest postcss@latest autoprefixer@latest

This worked fine. But when I run npm run dev I get this error:

ERROR in ./resources/assets/css/tailwindcore.css Module build failed (from ./node_modules/css-loader/index.js): ModuleBuildError: Module build failed (from ./node_modules/postcss-loader/src/index.js): Error: PostCSS plugin tailwindcss requires PostCSS 8.

I have read from the docs that PostCSS 8 is now required with tailwind 3. However, PostCSS 8 has been installed. Why would I still receive this error? I also tried to remove node_modules folder and reinstall, but got same error.

This is my package.json:

Many programming languages today have happens-before relation and release+acquire synchronization operations.

Some of these programming languages:

• C/C++11: happens-before, release+acquire
• Rust and Swift adopted the C/C++ memory model in its entirety — so they have that too.
• Java: happens-before, release+acquire.

I would like to know if release+acquire can violate happens-before:

• if it's possible, then I would like to see an example
• if it's impossible, then I would like to get simple and clear explanations why

Release/acquire establishes happens-before relation between different threads: in other words everything before release in Thread 1 is guaranteed to be visible in Thread 2 after acquire:

My understanding is that the typical notion of equality is too weak to prove many intuitive equalities on possibly infinite coinductive terms. Therefore it is necessary to introduce a coinductive equality for the specific coinductive type in question.

For instance, I have the following coinductive definitions concerning infinite relation transition sequences: