pluto-demo.jl

### A Pluto.jl notebook ###
# v0.19.9

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 4ea35bac-d47b-4258-9609-e783ee6fc09d
begin
	using PlutoUI
	using Random
	using SoleLogics
end

# ╔═╡ 12eb8901-7977-4eca-a701-e3b9430c3d36
# Instantiate a frame with 5 worlds and 5 edges
begin
	using Graphs

	worlds = SoleLogics.World.(1:5)
	edges = Edge.([(1,2), (1,3), (2,4), (3,4), (3,5)])
	fr = SoleLogics.ExplicitCrispUniModalFrame(worlds, Graphs.SimpleDiGraph(edges))
end

# ╔═╡ 617e413b-dcc2-4e43-a39c-54a90d20a074
md"""
## Propositional Logic
"""

# ╔═╡ 34342f5e-59a1-4442-8d7d-0bb74b8f4f4d
# An atom is a wrapper for anything representing a fact
Atom("I am alive")

# ╔═╡ 48c4a3c2-2334-4f8b-8288-cfa3a8ef7fb9
# Create atoms
p, q = Atom.(["p", "q"])

# ╔═╡ 6c7f587e-7aa8-4bf2-adfb-22b315d071e7
# Manually compose a formula
φ = ¬(p ∧ q)

# ╔═╡ b762a0a4-dff0-4cca-8324-e74f19406a1f
# Instantiate a propositional interpretation
I = TruthDict(["p" => true, "q" => false])

# ╔═╡ feaff836-9899-41b3-914b-3b84e831ea37
# Check the formula on the interpretation
check(φ, I)

# ╔═╡ addfbcaf-78f6-415e-aa09-7adb1d08d363
begin
	# Produce string representations of the formula
	println("Plain:\t\t\t\t\t" * syntaxstring(φ))
	println("Function notation:\t\t" * syntaxstring(φ; function_notation = true))
	println("With mare paretheses:\t" * syntaxstring(φ; remove_redundant_parentheses = false))
end

# ╔═╡ 2cf7d4ac-3267-4427-957b-d9ca4024e724
# Parse a formula from string
φ2 = parseformula("¬(p ∧ q)")

# ╔═╡ 7c9d5c28-f237-4b30-83a0-e3a84d0fd5ab
# Parse a formula with integer atoms
φ3 = parseformula("¬(1 ∧ 2)"; atom_parser = (x -> Atom(parse(Int64, x))))

# ╔═╡ 9da1c680-84a2-400e-a474-8a5c967bd445
@bind treeheight PlutoUI.Slider(1:10; default = 3)

# ╔═╡ a1ebd2cb-4677-4839-88c0-f3c57b08a1ab
begin
	println("Producing formula of height $treeheight...")

	# Create a random formula
	φ4 = randformula(Random.MersenneTwister(107), treeheight, [p,q], SoleLogics.BASE_PROPOSITIONAL_CONNECTIVES)

	φ4 |> syntaxstring |> println

	println("Simplifying...")

	# Minimize the formula (according to pre-defined, simple rules, e.g., De Morgan)
	normalize(φ4) |> syntaxstring |> println
end

# ╔═╡ 996c3107-ab3f-4fc9-a9f1-4b95a634bfde
# Define a new logical operator `⊕`
begin
	import SoleLogics: iscommutative, arity
	const ⊕ = SoleLogics.NamedConnective{:⊕}()
	SoleLogics.iscommutative(::typeof(⊕)) = true
	SoleLogics.arity(::typeof(⊕)) = 2

	# Compose a formula with `⊕`
	parseformula("¬p ∧ q") ⊕ p |> syntaxstring |> println

	# Generate a random formula with the new operator `⊕`
	φnew = randformula(Random.MersenneTwister(5), 2, [p,q], [¬, ∨, ⊕])

    φnew |> syntaxstring |> println
end

# ╔═╡ b226299d-57f7-481e-97a7-f51796f266a3
# Give XOR semantics to the operator `⊕`
begin
	import SoleLogics: collatetruth
    function SoleLogics.collatetruth(::typeof(⊕), (t1, t2)::NTuple{2,BooleanTruth})
        return Base.xor(istop(t1), istop(t2)) ? TOP : BOT
    end
	check(φnew, I)
end

# ╔═╡ 7342f90f-ee76-4d44-8925-d8019fc3e7e7
md"""
## Modal Logic
"""

# ╔═╡ b7b0094f-cfae-43ef-a8dc-4a3150e33339
# Generate a random MODAL formula
φmodal = randformula(Random.MersenneTwister(14), 3, [p,q], SoleLogics.BASE_MODAL_CONNECTIVES)

# ╔═╡ 66f9221f-294d-46d3-9ea7-a68a78216bb6


# ╔═╡ 11eee72d-5434-4153-82ed-c3e259c82f6f
# Enumerate the world that are accessible from the first world
accessibles(fr, first(worlds))

# ╔═╡ d9dcb925-1308-4981-9da9-43714385c72d
begin
	# Assign each world a propositional interpretation
	valuation = Dict([
	        worlds[1] => TruthDict([p => true, q => false]),
	        worlds[2] => TruthDict([p => true, q => true]),
	        worlds[3] => TruthDict([p => true, q => false]),
	        worlds[4] => TruthDict([p => false, q => false]),
	        worlds[5] => TruthDict([p => false, q => true]),
	     ])

	# Instantiate a Kripke structure
	K = KripkeStructure(fr, valuation)

	# Check the formula on each world of the Kripke structure
	[w => check(φmodal, K, w) for w in worlds]
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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[compat]
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"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

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deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
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version = "0.9.4"

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git-tree-sha1 = "62735db76083b47f80d292a874f7cdf353b1577f"
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[[deps.TableTraits]]
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version = "1.10.0"

[[deps.Test]]
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[[deps.ThreadSafeDicts]]
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version = "0.1.3"

[[deps.Tricks]]
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[[deps.URIs]]
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uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.5.0"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.Zlib_jll]]
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[[deps.libblastrampoline_jll]]
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[[deps.nghttp2_jll]]
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[[deps.p7zip_jll]]
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uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"
"""

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