PlusLink
The PlusLink, MinusLink, TimesLink and DivideLink are special cases of FunctionLinks that can be used to symbolically represent arithmetic formulas in the AtomSpace, as well as performing actual numeric computations.
Together with GreaterThanLink and EqualLink, they implement a basic theory of arithmetic.
These link types can be used both to represent arithmetic formulas, as graphs, so that symbolic manipulations can be performed, and also as active, functional elements that actually perform arithmetic computations.
These four arithmetic operations act component-wise on vectors. The AccumulateLink sums vector components.
Execution
For example, the knowledge graph of "2+3" can be expressed in Atomese as
(PlusLink (NumberNode 2) (NumberNode 3)))
It can also be directly executed, to obtain an a numeric result:
(cog-execute! (PlusLink (NumberNode 2) (NumberNode 3)))
will yield
(NumberNode "5.000000")
as a result. Note that both the formula, and the resulting answer are stored as atoms in the AtomSpace. Computations can be performed on FloatValues and TruthValues as well.
Numerical computation
Besides NumberNodes, the arithmetic links can perform computations on FloatValues and TruthValues. Thus, they can be used to "flow" numeric data through the knowledge graph. See FormulaPredicateLink for a basic example, and the /examples/atomspace/formulas.scm for a detailed tutorial.
Symbolic Representation and Reduction
The PlusLink and MinusLink (and all the other arithmetic link types) are useful for representing numeric knowledge in a form that can be algebraically manipulated, reasoned with, subjected to analysis and logical inference, and general symbolic manipulation.
The cog-execute! function can perform some basic algebraic reduction on arithmetic links. Thus, for example:
(cog-execute! (PlusLink (VariableNode "$x") (NumberNode 2) (NumberNode 3)))
will return
(PlusLink
(VariableNode "$x")
(NumberNode 5)
PlusLink and TimesLink both use FoldLink to do reduction of repeated terms.
More reduction examples
The current implementation of symbolic reduction is not terribly powerful (interested parties are invited to take it to the next level), but it can do a many basic reductions. The following should work.
(cog-execute! (PlusLink (NumberNode 0) (VariableNode "$x")))
and also
(cog-execute! (PlusLink
(NumberNode 2)
(VariableNode "$x")
(NumberNode -2)))
will both return
(VariableNode "$x")
Multiple addition is reduced to multiplication:
(cog-execute!
(PlusLink
(VariableNode "$x")
(VariableNode "$x")))
will return
(TimesLink (VariableNode "$x") (NumberNode "2"))
The post-ordering of numbers after variables is a convention coded in the reduct code.
Implementation
The PlusLink and TimesLink are implemented on top of FoldLink, which roughly corresponds to the generic comp-sci concept of folding as a specific kind of iterated associative operation applied to a list.
