Propositional Logic

Summary

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

Data types

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 \(x+y+z \ge 1\).

puan.logic.plog.AtMost : AtMost is a compound proposition which takes propositions and represents a lower 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 \(-x-y-z \ge -2\).

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).

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).

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")).

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.

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

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).

AtLeast

AtMost

All

Any

Imply

Xor

XNor

Not

PropositionValidationError

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Miscellaneous functions