The Łukasiewicz fuzzy m-semiring over double. More...

#include "Lukasiewicz.h"

Inheritance diagram for semiring::Lukasiewicz:

Collaboration diagram for semiring::Lukasiewicz:

Public Member Functions
virtual value_type	zero () const override
	Return the additive identity \(\mathbb{0}\).
virtual value_type	one () const override
	Return the multiplicative identity \(\mathbb{1}\).
virtual value_type	plus (const std::vector< value_type > &v) const override
	Apply the additive operation to a list of values.
virtual value_type	times (const std::vector< value_type > &v) const override
	Apply the multiplicative operation to a list of values.
virtual value_type	monus (value_type x, value_type y) const override
	Apply the monus (m-semiring difference) operation.
virtual value_type	delta (value_type x) const override
	Apply the \(\delta\) operator.
virtual bool	absorptive () const override
	Return `true` if this semiring is absorptive ( \(\mathbb{1} \oplus a = \mathbb{1}\) for all \(a\)).
virtual bool	compatibleWithBooleanRewrite () const override
	No semiring homomorphism `BoolFunc(Y)` →+* Lukasiewicz exists (the Łukasiewicz t-norm is not idempotent), so the safe-query Boolean rewrite is unsound under this semiring.
value_type	parse_leaf (const char *v) const
Public Member Functions inherited from semiring::Semiring< double >
virtual value_type	cmp (value_type s1, ComparisonOperator op, value_type s2) const
	Evaluate a comparison gate.
virtual value_type	semimod (value_type x, value_type s) const
	Apply a semimodule scalar multiplication.
virtual value_type	agg (AggregationOperator op, const std::vector< value_type > &s)
	Evaluate an aggregation gate.
virtual value_type	value (const std::string &s) const
	Interpret a literal string as a semiring value.
virtual	~Semiring ()=default

Additional Inherited Members
Public Types inherited from semiring::Semiring< double >
typedef double	value_type
	The carrier type of this semiring.

Detailed Description

The Łukasiewicz fuzzy m-semiring over double.

Each gate evaluates to a degree of evidence in \([0,1]\) under the Łukasiewicz t-norm.

Definition at line 57 of file Lukasiewicz.h.

Member Function Documentation

◆ absorptive()

virtual bool semiring::Lukasiewicz::absorptive ( ) const

inlineoverridevirtual

Return true if this semiring is absorptive ( \(\mathbb{1} \oplus a = \mathbb{1}\) for all \(a\)).

When true, the circuit evaluator and HAVING-semantics machinery may exploit the resulting idempotency ( \(a \oplus a = a\), implied by absorptivity) to deduplicate children of plus gates and to short-circuit over the multiplicative identity.

Returns: false by default; override to return true.

Reimplemented from semiring::Semiring< double >.

Definition at line 84 of file Lukasiewicz.h.

◆ compatibleWithBooleanRewrite()

virtual bool semiring::Lukasiewicz::compatibleWithBooleanRewrite ( ) const

inlineoverridevirtual

No semiring homomorphism BoolFunc(Y) →+* Lukasiewicz exists (the Łukasiewicz t-norm is not idempotent), so the safe-query Boolean rewrite is unsound under this semiring.

Inherits the false default from Semiring; this override exists for documentation.

Lean: Provenance.Semirings.Lukasiewicz.no_hom_from_BoolFunc (provenance-lean/Provenance/Semirings/Lukasiewicz.lean).

Reimplemented from semiring::Semiring< double >.

Definition at line 97 of file Lukasiewicz.h.