CLGC

A Python package to translate First-Order Logic (FOL) into different knowledge representation languages

Scope

A package used for handling logic statements and logic analysis using formal knowledge representation languages.

Key Features

• Translate FOL statements to other formal Knowledge Representation (KR) languages
• Categorize syllogisms by type

Supported KR Languages

• Common Logic Interchange Format (CLIF)
• Conceptual Graph Interchange Format (CGIF)
• Tensor Function Logic (TFL)
• Tensor Function Logic Plus (TFL+)
• CLINGO
• MINIFOLX
• PROLOG

Setup

Start by installing the package

pip install clgc

Then install the dependencies

pip install -r requirements.txt

Basic Usage

To load all functionalities

from clgc.__base import *

To create a valid syllogism in FOL, each statement of the syllogism should be followed by the '\n' terminator. The following example creates a syllogism of 2 premises and a conclusion:

syllogism = FOLSyllogism("∀x (Bikes(x) → ¬Calledcars(x))\n ∀x (Bike(x) → Vehicle(x))\n ∃x (Vehicles(x) ∧ Bikes(x))\n")

To categorize syllogisms in natural language or first-order language

syllogism = FOLSyllogism("∀x (Bikes(x) → ¬Calledcars(x))\n ∀x (Bike(x) → Vehicle(x))\n ∃x (Vehicles(x) ∧ Bikes(x))\n")

print
(syllogism.categorize())
# categorical

To translate from first-order language to another language (here, TFL+)

# get syllogism as text
test_syllogism = FOLSyllogism("∀x (Bikes(x) → ¬Calledcars(x))\n ∀x (Bike(x) → Vehicle(x))\n ∃x (Vehicles(x) ∧ Bikes(x))\n").syllogism
# convert to desired logical notation - here TFL+
tfl_plus_syllogism = FOLSyllogism.fol_to_tfl_plus(test_syllogism)

print(tfl_syllogism)
# -(+B0--+C0)-(+B0-+V0)+(+V1++B1)

A list of functions are available to modify a syllogism:

• add_statements (automatically adds the given statements in that order meaning the last given statement becomes the conclusion of the syllogism)
• add_premises (automatically keeps the original conclusion and adds everything given as premises)
• add_conclusion (automatically takes the given statement as the conclusion and renders everything else to premises)

An example of adding new statements

test_syllogism = FOLSyllogism("∃x (Canine(x) ∧ ¬AquaticCreatureKnownAsFish(x))\n")
        test_syllogism.add_statements(["∀x (Fish(x) → ¬MammalThereforeEveryCanineFallUnderTheCategoryOfMammal(x))\n"])   

print(test_syllogism.statements)
# ["∃x (Canine(x) ∧ ¬AquaticCreatureKnownAsFish(x))", "∀x (Fish(x) → ¬MammalThereforeEveryCanineFallUnderTheCategoryOfMammal(x))"])

An example of adding new premises

test_syllogism = FOLSyllogism("∃x (Canine(x) ∧ ¬AquaticCreatureKnownAsFish(x))\n ∀x (Bike(x) → Vehicle(x))\n")
        test_syllogism.add_premises(["∀x (Fish(x) → ¬MammalThereforeEveryCanineFallUnderTheCategoryOfMammal(x))\n"]) 

print(test_syllogism.premises)
# ["∃x (Canine(x) ∧ ¬AquaticCreatureKnownAsFish(x))", "∀x (Fish(x) → ¬MammalThereforeEveryCanineFallUnderTheCategoryOfMammal(x))"]

An example of adding a new conclusion

test_syllogism = FOLSyllogism("∃x (Canine(x) ∧ ¬AquaticCreatureKnownAsFish(x))\n ∀x (Bike(x) → Vehicle(x))\n")
        test_syllogism.add_conclusion("∀x (Fish(x) → ¬MammalThereforeEveryCanineFallUnderTheCategoryOfMammal(x))\n") 

print(test_syllogism.conclusion)
# "∀x (Fish(x) → ¬MammalThereforeEveryCanineFallUnderTheCategoryOfMammal(x))"