Logical

class pba.logical.Logical

Bases: Interval

Represents a logical value that can be either True or False or dunno ([False,True]).

Inherits from the Interval class.

Attributes:

left (bool): The left endpoint of the logical value.

right (bool): The right endpoint of the logical value.

Attributes:

left: The left boundary of the interval.

right: The right boundary of the interval.

Default values

If only 1 argument is given then the interval is assumed to be zero width around this value.

If no arguments are given then the interval is assumed to be vaccous (i.e. \([-\infty,\infty]\)). This is implemented as Interval(-np.inf,np.inf).

__init__(left: bool, right: bool | None = None)

Attributes:

left: The left boundary of the interval.

right: The right boundary of the interval.

Default values

If only 1 argument is given then the interval is assumed to be zero width around this value.

If no arguments are given then the interval is assumed to be vaccous (i.e. \([-\infty,\infty]\)). This is implemented as Interval(-np.inf,np.inf).

pba.logical.always(logical: Logical | Interval | Number | bool) → bool

Checks whether the logical value is always true. i.e. Every value from one interval or p-box is always greater than any other values from another.

This function takes either a Logical object, an interval or a float as input and checks if both the left and right attributes of the Logical object are True. If an interval is provided, it checks that both the left and right attributes of the Logical object are 1. If a numeric value is provided, it checks if the is equal to 1.

Parameters:

logical (Logical, Interval , Number): An object representing a logical condition with ‘left’ and ‘right’ attributes, or a number between 0 and 1.

Returns:

bool: True if both sides of the logical condition are True or if the float value is equal to 1, False otherwise.

Error

TypeError: If the input is not an instance of Interval, Logical or a numeric value.

ValueError: If the input float is not between 0 and 1 or the interval contains values outside of [0,1]

Examples:

>>> a = Interval(0, 2)
>>> b = Interval(1, 3)
>>> c = Interval(4, 5)
>>> always(a < b)
False
>>> always(a < c)
True

pba.logical.is_same_as(a: Pbox | Interval, b: Pbox | Interval, deep=False, exact_pbox=True)

Check if two objects of type ‘Pbox’ or ‘Interval’ are equal.

Parameters:

a: The first object to be compared.

b: The second object to be compared.

deep: If True, performs a deep comparison, considering object identity. If False, performs a shallow comparison based on object attributes. Defaults to False.

exact_pbox: If True, performs a deep comparison of p-boxes, considering all attributes. If False, performs a shallow comparison of p-boxes, considering only the left and right attributes. Defaults to True.

Returns True if:

bool: True if the objects have identical parameters. For Intervals this means that left and right are the same for both a and b. For p-boxes checks whether all p-box attributes are the same. If deep is True, checks whether the objects have the same id.

Examples:

>>> a = Interval(0, 2)
>>> b = Interval(0, 2)
>>> c = Interval(1, 3)
>>> is_same_as(a, b)
True
>>> is_same_as(a, c)
False

For p-boxes:

>>> a = pba.N([0,1],1)
>>> b = pba.N([0,1],1)
>>> c = pba.N([0,1],2)
>>> is_same_as(a, b)
True
>>> is_same_as(a, c)
False
>>> e = pba.box(0,1,steps=2)
>>> f = Pbox(left = [0,0],right=[1,1],steps=2)
>>> is_same_as(e, f, exact_pbox = True)
False
>>> is_same_as(e, f, exact_pbox = False)
True

pba.logical.never(logical: Logical) → bool

Checks whether the logical value is always true. i.e. Every value from one interval or p-box is always less than any other values from another.

This function takes either a Logical object, an interval or a float as input and checks if both the left and right attributes of the Logical object are False. If an interval is provided, it checks that both the left and right attributes of the Logical object are 0. If a numeric value is provided, it checks if the is equal to 0.

Parameters:

logical (Logical, Interval , Number): An object representing a logical condition with ‘left’ and ‘right’ attributes, or a number between 0 and 1.

Returns:

bool: True if both sides of the logical condition are True or if the float value is equal to 0, False otherwise.

Error

TypeError: If the input is not an instance of Interval, Logical or a numeric value.

ValueError: If the input float is not between 0 and 1 or the interval contains values outside of [0,1]

Examples:

>>> a = Interval(0, 2)
>>> b = Interval(1, 3)
>>> c = Interval(4, 5)
>>> never(a < b)
False
>>> never(a < c)
True

pba.logical.sometimes(logical: Logical) → bool

Checks whether the logical value is sometimes true. i.e. There exists one value from one interval or p-box is less than a values from another.

This function takes either a Logical object, an interval or a float as input and checks if either the left and right attributes of the Logical object are True. If an interval is provided, it that both endpoints are not 0. If a numeric value is provided, it checks if the is not equal to 0.

Parameters:

logical (Logical, Interval , Number): An object representing a logical condition with ‘left’ and ‘right’ attributes, or a number between 0 and 1.

Returns:

bool: True if both sides of the logical condition are True or if the float value is equal to 0, False otherwise.

Error

TypeError: If the input is not an instance of Interval, Logical or a numeric value.

ValueError: If the input float is not between 0 and 1 or the interval contains values outside of [0,1]

Examples:

>>> a = pba.Interval(0, 2)
>>> b = pba.Interval(1, 4)
>>> c = pba.Interval(3, 5)
>>> pba.sometimes(a < b)
True
>>> pba.sometimes(a < c)
True
>>> pba.sometimes(c < b)
True

pba.logical.xtimes(logical: Logical) → bool

Checks whether the logical value is exclusively sometimes true. i.e. There exists one value from one interval or p-box is less than a values from another but it is not always the case.

This function takes either a Logical object, an interval or a float as input and checks that the left value is False and the right value is True If an interval is provided, it that both endpoints are not 0 or 1. If a numeric value is provided, it checks if the is not equal to 0 or 1.

Parameters:

logical (Logical, Interval , Number): An object representing a logical condition with ‘left’ and ‘right’ attributes, or a number between 0 and 1.

Returns:

bool: True if both sides of the logical condition are True or if the float value is equal to 0, False otherwise.

Error

TypeError: If the input is not an instance of Interval, Logical or a numeric value.

ValueError: If the input float is not between 0 and 1 or the interval contains values outside of [0,1]

Examples:

>>> a = pba.Interval(0, 2)
>>> b = pba.Interval(2, 4)
>>> c = pba.Interval(2.5,3.5)
>>> pba.xtimes(a < b)
False
>>> pba.xtimes(a < c)
False
>>> pba.xtimes(c < b)
True