A sentence is an atomic sentence or a (compound) sentence. An atomic sentence consists of a predicate and constants the predicate has as its arguments. The set of constants is single-sorted. There is no variable, no function. The number of arguments of a predicate is called the arity of the predicate. A compound sentence can be obtained by joining sentences with connectives.
pystc is a simple but extensible Python module for sentences.
It provides functionality to define sentences as you like
by adding constants, predicates, and connectives, whether logical or non-logical.
Constants, predicates, and connectives can be introduced by specifying
their names and how they are associated with other well-defined objects or
functions.
$ pip install pystc
Let us first create atomic sentences that can be built from a predicate =
and constants T, F,
from pystc import AtomicSentence
# Let us add predicate "=" so that the arity for it is 2.
AtomicSentence.add_predicate("=",2)
AtomicSentence.add_constant("T")
AtomicSentence.add_constant("F")
# Now, sentences are ready to create.
s1 = AtomicSentence("=","T","T")
s2 = AtomicSentence("=","T","F")
s3 = AtomicSentence("=","F","T")
assert str(s2) == "=(T,F)"
assert AtomicSentence.read("=(T,F)") == s2Let us next construct compound sentences.
A Sentence in pystc module is simply a recursive type defined to be:
Sentence = Union[str, AtomicSentence, Tuple["Sentence"]]Although it is loosely defined for simplicity, sentences are implicitly expected to fall into one of the following cases:
1. An AtomicSentence object, say s2.
1. The string representation of an AtomicSentence object, say "=(T,F)".
1. A tuple such that the initial entry is a connective name and the other entries are Sentence objects, say ("&", s2, ("!", s2)).
As the connective names "&" and "!" appears just above,
let us introduce these connectives in the following codeblock
and inteprete sentences.
from pystc import SentenceConverter
# Let us set an atomic sentence type and how each symbol is interpreted.
SentenceConverter.set_atom_type(AtomicSentence)
SentenceConverter.set_constant_destination("T", True)
SentenceConverter.set_constant_destination("F", False)
SentenceConverter.set_predicate_destination("=", lambda li,w: li[0]==li[1])
SentenceConverter.set_connective_destination("&",lambda li,w: not False in li)
SentenceConverter.set_connective_destination("|",lambda li,w: True in li)
SentenceConverter.set_connective_destination("!",lambda li,w: not li[0])
assert SentenceConverter.convert(s2) == False
assert SentenceConverter.convert("=(T,F)") == False
assert SentenceConverter.convert(("&", s2, ("!", s2))) == False
assert SentenceConverter.convert(("&", "=(T,F)", ("!", s2))) == FalseFor another example of usage, let us convert sentences into strings in infix notation.
# Clear all class variables
SentenceConverter.clear()
SentenceConverter.set_atom_type(AtomicSentence)
SentenceConverter.set_constant_destination("T", "T")
SentenceConverter.set_constant_destination("F", "F")
SentenceConverter.set_predicate_destination("=", lambda li,w: f"{li[0]}={li[1]}")
SentenceConverter.set_connective_destination("&",lambda li,w: "("+" & ".join(li)+")")
SentenceConverter.set_connective_destination("|",lambda li,w: "("+" | ".join(li)+")")
SentenceConverter.set_connective_destination("!",lambda li,w: "!"+li[0])
assert SentenceConverter.convert("=(T,F)") == "T=F"
assert SentenceConverter.convert(("&", s2, ("!", s2))) == "(T=F & !T=F)"Let us not forget to clear class variables after everything is finished.
SentenceConverter.clear()
AtomicSentence.clear()Please report bugs and requests from GitHub Issues , and ask questions from GitHub Discussions .
Please see LICENSE .