language-ext modal logic in csharp

To model modal logic in C#, you can use the functional programming library LanguageExt which provides a set of monads and applicative functors.

First, you would need to define a type that represents a proposition. For example:


main.cs
public record Proposition(string Name);
40 chars
2 lines

Then, you can define a modal operator as a function that takes a proposition and returns a new proposition that represents the proposition being true in a given world. For example, the "necessarily" modal operator can be defined as follows:


main.cs
public delegate Prop Necessarily<Prop>(Prop prop);

// Example usage:
Necessarily<Proposition> necessarily = prop => new Proposition($"◻{prop.Name}");
Proposition p = new Proposition("p");
Proposition necessarilyP = necessarily(p); // Creates a new proposition "◻p"
266 chars
7 lines

Next, you can define a set of worlds which represent the different states of the world. For example:


main.cs
public record World(string Name);
34 chars
2 lines

Then, you can define a type that represents a modal formula, which is a proposition that is either true or false in a given set of worlds. You can use the Option monad from LanguageExt to represent the truth value of a formula in a world.


main.cs
using LanguageExt;

public record ModalFormula(Proposition Prop, Func<World, Option<bool>> IsTrueIn);

// Example usage:
ModalFormula formula = new Proposition("p").ToModalFormula(
    world => world.Name == "w1" ? Some(true) :
             world.Name == "w2" ? Some(false) :
             Option<bool>.None);
bool? isPTrueInW1 = formula.IsTrueIn(new World("w1")).IfNone(null); // Returns true
bool? isPTrueInW2 = formula.IsTrueIn(new World("w2")).IfNone(null); // Returns false
bool? isPTrueInW3 = formula.IsTrueIn(new World("w3")).IfNone(null); // Returns null
562 chars
13 lines

Finally, you can define a set of inference rules that allow you to reason about the truth value of a modal formula in different sets of worlds. For example, the rule of necessitation states that if a formula is true in all possible worlds, then it is necessarily true:


main.cs
public static class ModalInferenceRules
{
    // Rule of necessitation
    public static ModalFormula Necessarily(this ModalFormula formula) =>
        new ModalFormula(formula.Prop, world =>
            formula.IsTrueIn(world).Match(
                Some: isTrue => isTrue ? Some(true) : Option<bool>.None,
                None: () => Option<bool>.None));
}
359 chars
10 lines

With all these components in place, you can now reason about modal logic formulas in C# using the LanguageExt library.

similar csharp code snippets

create s5 modal logic in csharp

create a s5 modal logic system class in csharp

design generic s5 modal logic system in csharp

make s5 modal logic class in csharp

create a generic modal logic class with list of items in csharp

make s5 modal logic model in csharp

make generic dynamic epistemic logic system in csharp

create a generic modal logic system class and ienumarable in csharp

create a generic modal logical system with linq in csharp

find the index of an element in an array in csharp

related categories