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Propositional Logic

Summary

Propositional Logic (plog) system is an abstract data type defining logical relationships between variables in a combinatorial optimization manner.

Data types

:class:`puan.logic.plog.AtLeast` : AtLeast is a compound proposition which takes propositions and represents a lower bound on the result of those propositions. For example, select at least one of x, y and z would be defined as AtLeast(propositions=["x","y","z"], value=1) and represented by the linear inequality x+y+z \ge 1.

:class:`puan.logic.plog.AtMost` : AtMost is a compound proposition which takes propositions and represents an upper bound on the result of those propositions. For example, select at most two of x, y and z would be defined as AtMost(propositions=["x","y","z"], value=2) and represented by the linear inequality -x-y-z \ge -2.

:class:`puan.logic.plog.Equal` : Equal is a compound proposition which takes propositions and represents an exact bound on the result of those propositions. For example, select propositions equal to two of x, y and z would be defined as Equal(propositions=["x","y","z"], value=2) and represented by the linear inequality x+y+z = -2.

:class:`puan.logic.plog.All` : All is a compound proposition representing a conjunction of all given propositions. All is represented by an AtLeast proposition with value set to the number of given propositions. For example, All("x","y","z") is equivalent to AtLeast(propositions=["x","y","z"], value=3).

:class:`puan.logic.plog.Any` : Any is a compound proposition representing a disjunction of all given propositions. Any is represented by an AtLeast proposition with value set to 1. For example, Any("x","y","z") is equivalent to AtLeast(propositions=["x","y","z"], value=1).

:class:`puan.logic.plog.Imply` : Imply is the implication logic operand and has two main inputs: condition and consequence. For example, if x is selected then y and z must be selected could be defined with the Imply class as Imply("x", All("y","z")).

:class:`puan.logic.plog.Xor` : Xor is restricting all propositions within to be selected exactly once. For example, Xor("x","y","z") means that one and exactly one of x, y and z must be selected.

:class:`puan.logic.plog.XNor` : XNor is a negated Xor. In the special case of two propositions, this is equivalent to the biconditional logical connective (<->).

:class:`puan.logic.plog.Not` : Not is negating a proposition. For example, Not(All("x","y","z")) means that x, y and z can never be selected all together and is equivalent to AtMost(propositions=["x","y","z"], value=2).

.. currentmodule:: puan.logic.plog

AtLeast

.. autoclass:: AtLeast
   :members:
   :undoc-members:
   :show-inheritance:

AtMost

.. autoclass:: AtMost
   :members:
   :undoc-members:
   :show-inheritance:

Equal

.. autoclass:: Equal
   :members:
   :undoc-members:
   :show-inheritance:

All

.. autoclass:: All
   :members:
   :undoc-members:
   :show-inheritance:

Any

.. autoclass:: Any
   :members:
   :undoc-members:
   :show-inheritance:

Imply

.. autoclass:: Imply
   :members:
   :undoc-members:
   :show-inheritance:

Xor

.. autoclass:: Xor
   :members:
   :undoc-members:
   :show-inheritance:

XNor

.. autoclass:: XNor
   :members:
   :undoc-members:
   :show-inheritance:

Not

.. autoclass:: Not
   :members:
   :undoc-members:
   :show-inheritance:

PropositionValidationError

.. autoclass:: PropositionValidationError
   :members:
   :undoc-members:
   :show-inheritance: