make a s5 modal logic into a class with property and list of axioms in csharp

To create a class for modal logic with a property and list of axioms, you can follow these steps:

1. Define a class ModalLogic with a property PropositionalVariables to store the set of propositional variables in the modal logic.

main.cs
public class ModalLogic {
    public HashSet<string> PropositionalVariables { get; set; }
}
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Here, we are using a HashSet<string> to store the set of propositional variables.

2. Next, define a class Axiom to represent individual axioms. Each Axiom object will have a Name property to describe the name of the axiom and a Formula property to store the logical formula associated with the axiom.

main.cs
public class Axiom {
    public string Name { get; set; }
    public string Formula { get; set; }
}
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3. Add a List<Axiom> property to the ModalLogic class to store the list of axioms.

main.cs
public class ModalLogic {
    public HashSet<string> PropositionalVariables { get; set; }
    public List<Axiom> Axioms { get; set; }
}
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4. You can now create an instance of the ModalLogic class and add axioms to it.

main.cs
var modalLogic = new ModalLogic();

modalLogic.PropositionalVariables = new HashSet<string> {
    "p", "q", "r"
};

modalLogic.Axioms = new List<Axiom> {
    new Axiom {
        Name = "Distribution",
        Formula = "[]p -> ([]q & []r) -> [] (p -> (q & r))"
    },
    new Axiom {
        Name = "Transitivity",
        Formula = "[]p -> [][]p"
    }
};
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Here, we are adding two axioms to the Axioms list property of the ModalLogic object.

By following the above steps, you can create a ModalLogic class with a property and list of axioms in C#.