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# NAME

CInet::Propositional - CI inference axioms and SAT solvers

# SYNOPSIS

    # Imports all related modules
    use CInet::Propositional;

## VERSION

This document describes CInet::Propositional v0.9.2.

# DESCRIPTION

This module imports all modules in its distribution, most notably
[CInet::Propositional::Syntax](/doc/CInet%3A%3APropositional%3A%3ASyntax) which defines the `propositional`
keyword. Using this keyword, families of CI relations can be
defined axiomatically using a syntax very close to mathematics:

    propositional Semigraphoids = cube (ijk|L) -> (ij|L) & (ik|jL) => (ij|kL) & (ik|L);

This results in a [CInet::Propositional::Type](/doc/CInet%3A%3APropositional%3A%3AType) object which can
be instantiated by giving a [CInet::Cube](/doc/CInet%3A%3ACube) object. This results
in a [CInet::Seq::Propositional](/doc/CInet%3A%3ASeq%3A%3APropositional) sequence representing all
[CInet::Relation](/doc/CInet%3A%3ARelation)s compatible with the axioms:

    say Semigraphoids(4)->count #= 26424

There are indeed 26424 semigraphoids on a 4-element ground set.
This number is obtained in the blink of an eye because the set
is defined axiomatically and by being a [CInet::Seq::Propositional](/doc/CInet%3A%3ASeq%3A%3APropositional),
a #SAT solver is used for counting.

# AUTHOR

Tobias Boege <tobs@taboege.de>

# COPYRIGHT AND LICENSE

This software is copyright (C) 2020 by Tobias Boege.

This is free software; you can redistribute it and/or
modify it under the terms of the Artistic License 2.0.