Using Formulae

LaTeX Rendering

Formulae can be rendered as LaTeX code, with the to_latex() method of Formula objects. Example:

>>> from logicalpy import Formula
>>> fml = Formula.from_string("(P -> (~P & P)) v Q")
>>> print(fml.to_latex())
$(P \to (\neg P \land P)) \lor Q$

The above LaTeX would render as follow: \((P \to (\neg P \land P)) \lor Q\)

Equality testing

Two formulae can be tested for equality with the normal Python equality testing syntax. Example:

>>> from logicalpy import Formula
>>> Formula.from_string("A & B") == Formula.from_string("A -> C")
False
>>> Formula.from_string("A v (B v C)") == Formula.from_string("A | (B | C)")
True

Note

This only tests if the propositions are exactly equal. For instance, two semantically equivalent formulae but with different structures will not be considered equal. Likewise, formulae with the same structure but with different proposition names will not be considered equal.

Formula Propositions

You can get the set of all the propositions of a formula with every proposition represented by its name (str) using the propositions() method of Formula objects:

>>> from logicalpy import Formula
>>> fml = Formula.from_string("P -> Q")
>>> fml.propositions()
{'P', 'Q'}

Semantic Valuation

Formula objects can be tested with a particular valuation, with the is_satisfied() method. This method takes a valuation as a dict associating each proposition name (str) with a truth value (bool) and returns whether the Formula is satisfied by the valuation. Example:

>>> from logicalpy import Formula
>>> fml = Formula.from_string("P & Q")
>>> fml.is_satisfied({"P": True, "Q": False})
False
>>> fml.is_satisfied({"P": True, "Q": True})
True

For a complete reference of the Formula class, see its API reference.