Framework for Fuzzy Logic Rule Definition

The module hybrid_learning.fuzzy_logic defines a framework to

• define (logical) operations as functions that accept a grounding and provide the rule truth value

• define (fuzzy) logic rules as computational trees of operations

• parse rules to and from string representation

• define logics as collections of operation builders

For details have a look at the API Reference and the user guide.

Base Classes

Merge	Base class for operations and operation trees on dictionary inputs.
TorchOrNumpyOperation	Generic merge operation allowing to define both a torch and a numpy operation.
Logic	Basic definition of a logic.
FormulaParser	Base class to parse string formula specifiers in infix notation to merge operations.

Standard Fuzzy Logics

The following (fuzzy) logics with standard connectives from Boolean or t-norms fuzzy logic are defined in hybrid_learning.fuzzy_logic.tnorm_connectives. Select one of them by key using hybrid_learning.fuzzy_logic.logic_by_name().

boolean.BooleanLogic	Boolean logic and parser.
product.ProductLogic	Product fuzzy logic parser.
lukasiewicz.LukasiewiczLogic	Lukasiewicz logic parser.
goedel.GoedelLogic	Goedel fuzzy logic parser.

Parsing

See FormulaParser.

Standard Connectives

fuzzy_common.NOT	Fuzzy logic NOT.
boolean.AND	Intersection/AND operation on binary masks and scalars.
boolean.OR	Union/OR operation on binary masks and scalars.
boolean.IMPLIES	Pixel-wise implication logical connective on binary masks and scalars.
boolean.IMPLIEDBY	Goedel inverted logic IMPLIES connective.
product.AND	Product AND operation.
product.OR	Product OR operation.
product.IMPLIES	Product logic IMPLIES connective.
product.IMPLIEDBY	Goedel inverted logic IMPLIES connective.
lukasiewicz.AND	Lukasiewicz AND operation.
lukasiewicz.OR	Lukasiewicz OR operation.
lukasiewicz.IMPLIES	Lukasiewicz logic IMPLIES connective.
lukasiewicz.IMPLIEDBY	Goedel inverted logic IMPLIES connective.
goedel.AND	Goedel or Minimum AND operation.
goedel.OR	Goedel or Maximum OR operation.
goedel.IMPLIES	Goedel logic IMPLIES connective.
goedel.IMPLIEDBY	Goedel inverted logic IMPLIES connective.

Standard Quantifiers

ALL	Reduce a single tensor along given dimensions using logical AND.
ANY	Reduce a single tensor along given dimensions using logical OR.
WHERE	Filter the dimensions in tensor a by the boolean values given in cond.

Predicates

Arithmetic Predicates

Equals	Predicate of arity 2 that checks element-wise equality between two arrays.
GreaterEqualsThan	Predicate of arity 2 that thresholds number values at a given threshold.
GreaterThan	Predicate of arity 2 that thresholds number values at a given threshold.
LowerEqualsThan	Predicate of arity 2 that checks whether an input is below or equals a threshold.
LowerThan	Predicate of arity 2 that checks whether an input is below a threshold.

Custom Operations

AllNeighbors	Given a mask of truth values representing the output of a formula apply average pooling.
BestIoUWith	Given two stacked sets of masks masks_a and masks_b, calculate for each mask in masks_a the best IoU with any mask in masks_b.
CoveredBy	Calculate the proportion of one mask covered by another.
IoUWith	Calculate the intersection over union between two masks.
IsPartOfA	Unary predicate that calculates for each pixel location whether it is part of an object segmentation.
LambdaOp	Provide a custom transformation on the sequence of values extracted from the annotations dict.