Updating the “If” statement in the JVM for Truth Value Logic

The Vital Development Kit (VDK) provides development tools and an API for Artificial Intelligence (AI) applications and data processing.  This includes a “Domain Specific Language” (DSL) for working with data.

To this DSL we’ve recently added an extension to the venerable “If” statement in the JVM to handle Truth Values. (Truth Values, see: Beyond True and False: Introducing Truth to the JVM )

The “If” statement is the workhorse of computer programming.  If this, do that.  If something is so, then do some action.  The “If” statement evaluates if some condition is “True”, and if so, takes some action.  If the condition is “False”, then it may take some other action.

The condition of an “If” statement yields a Boolean True or False and typically involves tests of variables, such as:  height > 72, speed < 50, name == “John”.

The “If” statement is a special case of the “switch” statement, such that:

if(name == "John") { do something }
else { do something different }

is the same as:

switch (name == "John") {
case true: { do something; break }
case false: { do something different; break }
}

In the VDK we have an extension of Boolean in the JVM called Truth.  Truth may take four values: YES, NO, UNKNOWN, or MU compared to the Boolean TRUE or FALSE.  YES and NO are the familiar TRUE and FALSE, with UNKNOWN providing a value for when a condition cannot be determined because of unknown inputs, and MU providing a value for when a condition is unknowable because it contains a false premise.

For example, for UNKNOWN, the color of a traffic light might be red, green, or yellow but its value is currently UNKNOWN.  And for MU, the favorite color of a traffic light is MU because inanimate objects don’t have favorite colors.

UNKNOWN and MU are part of the familiar Boolean Truth Tables.  For instance True AND True yields True, whereas True AND Unknown yields Unknown.

Details of the Truth implementation in the JVM can be found in the blog post: Beyond True and False: Introducing Truth to the JVM

Because Truth has four values, we need a way to handle four cases when we test a condition.

As above, we could use a “switch” statement like so:

switch (Truth Condition) {
case YES: { handle YES; break }
case NO: { handle NO; break }
case UNKNOWN: { handle UNKNOWN; break }
case MU: { handle MU; break }
} 

This is a little verbose, so we’ve introduced a friendlier statement: consider.

consider (Truth Condition) {
YES: { handle YES }
NO: { handle NO }
UNKNOWN: { handle UNKNOWN }
MU: { handle MU }
} 

So we can have code like:

consider (trafficlight.color == GREEN) {
YES: { car.drive() }
NO: { car.stop() }
UNKNOWN: { car.stop() } // better be safe and look around
MU: { car.stop(); runDiagnostics(); } // error! error!
} 

In the above code, if evaluating our truth condition results in an UNKNOWN value (perhaps a sensor cannot “see” the Traffic Light), we can take some safe action.  If we get a MU value, then we have some significant error, such the “trafficlight” object not actually being a trafficlight — perhaps some variable mixup.  We can also take some defensive measures in this case.

We can also stick with using “If” and use exceptions for the cases of UNKNOWN and MU:

try {
if(trafficlight.color == GREEN) { car.drive() }
else { car.stop() }
} catch(Exception ex) {
// handle UNKNOWN and MU
}

This works because Truth values are coerced to Boolean True or False for the cases of YES or NO.  This coercion throws an exception for the cases of UNKNOWN or MU.  JVM exceptions are a bit ugly and should not be used for normal program control flow (exceptions as flow control is often an anti-pattern), so the consider statement is much preferred.

The logic of Truth is very helpful in defining Rules to process realtime dynamic data, and answer dynamic data queries.  The consider statement allows such rules to be quite succinct and explicitly handle unknown data or queries with non-applicable conditions.

For instance, if we query an API for the status of traffic lights and ask how many are currently yellow, we might get back a reply of 0 (zero).  We might wonder are there really zero traffic lights yellow presently, or is the API not functioning and always returning zero, or does it not track yellow lights?  It would be better to get a reply of UNKNOWN if the API was not functioning.  If we asked how many traffic lights were displaying Purple, a reply of zero would be correct but it would be better to get a reply of MU –  there are no such thing as Purple traffic lights in a world of Red/Yellow/Green lights.

As AI and data-driven applications incorporate more dynamic data models and data sources, instances of missing or incorrect knowledge are more the rule rather than the exception, so the software flow should treat these as normal cases to consider rather than exceptions.

Hope you have enjoyed learning about how the Vital Development Kit has extended “If” to handle Truth Values.  Please post and questions or comments below, or get in touch with us at info@vital.ai.

Beyond True and False: Introducing Truth to the JVM

In this post we introduce a new type for “Truth” to the JVM in the Vital Development Kit (VDK), to include cases that don’t fit into Boolean True and False — in particular a value for Unknown and Mu (nonexistence).  We use this new Truth type in the VDK for logical and conditional expressions, especially in rules and inference.

Computer hardware has binary — ones and zeros.
Computer software has boolean — true and false.
This seems a perfect match, immutable, a Platonic Ideal.
But there are some wrinkles.

Programming languages deeply use booleans to control the flow of a program:

if this is true, then do that
if this is false, then do something else

What if the software doesn’t know a particular value at that moment?

What if the value doesn’t make sense in the current context?

For instance, in the code:

if(TrafficLight.color == RED) then { Stop() }
else { Go() }

What if the TrafficLight color is unknown?  The software would drive through the traffic intersection.  (Hope for the best!)

Or, what if we had code like:

if(Penguin.flightspeed < 10) then { ThrowAFish() }

Should this code work, even if penguins don’t have a flight speed?

In programming languages like Java, these problems lead to a lot of custom workarounds and error checking, so much so that you can no longer use “normal” boolean expressions without a bunch of checks to ensure that it is “safe”.

In rule-based systems or logic languages, often “unknown” is treated as False — this is because a rule like isTall(John) tries to prove that John is tall, and if it can’t it returns “false” or “no”, meaning “I can not prove that”.

But, if the code re-uses that result like:

isShort(X) := NOT isTall(X)

then it is incorrectly combining the Is-Tall case with the I-Don’t-Know case, causing software errors — that is, if the height is unknown, then the person is short, which is quite a leap of logic to be sure.

Three Value Logic

This is not a new problem.  SQL tries to solve this with a third logic value called NULL to mean “UNKNOWN”.  A description of this is here: https://en.wikipedia.org/wiki/Null_(SQL)

Three value logic (3VL) for True/False/Unknown is well established, with a full description here: https://en.wikipedia.org/wiki/Three-valued_logic

Unfortunately 3VL is not built into languages like Java.  And, it gets worse.

Java has low level base types that are efficient like int for integers and object-oriented classes like Integer which have some additional Object overhead but are more “friendly”, and there are ways to convert between Objects and base types.  So far, so good.

All objects (instances of classes) may be set to the value of “null”.  There is a class for Boolean which may be set to True, False, or Null.  And, there is the low-level type “boolean” which may only have the values of true and false.  So a Boolean object has a value (“null”) which can not be set in the base type boolean.  It is like having a base type for integer that you can’t set to zero.

(Mis)Using Null as a Value

In Java, “null” means uninitialized and is not a true distinct “value”.   Some code uses (abuses) “null” to mean “unknown”, but this means we then can’t tell apart an uninitialized value from a initialized “unknown” value — similar to confusing “I-can’t-prove-it” with “false”.  Moreover, we can’t store “null” in the low level boolean type anyway, which again can only be true or false.

1aab4d13e65d4c245d46c0ab4679ffa7
“If that is okay, please give me absolutely no sign.”

The value of “null” also occurs in lots of error situations — the network connection failed, the database connection timed out, the password is incorrect, no memory is available, and on and on.

Using “null” as a value reminds me of this Simpon’s line with Homer interpreting the absence of a message (“null”) as a message.

So, the addition of “null” to Java’s Boolean doesn’t provide a way to represent “unknown” unambiguously, and it causes even more confusion with uninitialized objects and various error conditions.

A Value for Nonexistence

Besides the “unknown” case there is also the case above of: Penguin.flightspeed < 10.

Since we know that a penguin can’t have a flightspeed, this isn’t a case of “unknown.”  We could argue that this statement of less than 10 is “true” since “0” is the absence of a speed and 0 is less than 10, but that requires embedding domain knowledge about how speeds work, i.e. Is the temperature of a song absolute zero? (-459.67F)  Is the color of an integer black?  There isn’t a universal way to assign these True or False when the question doesn’t make sense.

500px-無-still.svg
Mu

And so, we need a fourth value to handle the case of “nonexistence” or “non-applicable”.

We’ve chosen to use the symbol Mu for this as it has been popularly been used in this sense.  One notable example of its use is in Douglas R. Hofstadter’s wonderful book:

Gödel, Escher, Bach: An Eternal Golden Braid.  (http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567)

Some more details regarding Mu are in its wikipedia article here: https://en.wikipedia.org/wiki/Mu_(negative)

 

Truth implementation in the VDK

In the VDK, we use the Groovy language for scripting on the JVM.  Truth was added as a new type to Groovy with the values: YES, NO, UNKNOWN, and MU.  We use YES and NO instead of True and False to avoid confusion with the existing Boolean values and reserved words.

We follow the truth tables as specified here for 3VL: https://en.wikipedia.org/wiki/Three-valued_logic#Kleene_and_Priest_logics

Some example logic statements using AND, OR, and NOT with Truth:

  • YES AND UNKNOWN := UNKNOWN
  • YES OR UNKNOWN := YES
  • NO OR UNKNOWN := UNKNOWN
  • NOT UNKNOWN := UNKNOWN

For Mu, any logic expression with Mu yields MU:

  • NOT MU := MU
  • YES OR MU := MU

Using our new Truth definition, we can now write or generate code that handles the cases of Unknown or Mu without any ambiguity.

For example:


Truth isTall(Person p) {
if( p.height == UNKNOWN ) { return UNKNOWN }
if  ( p.height > 72.0)  { return YES }
else { return NO }
}

Truth isShort(Person p) {
if( p.height == UNKNOWN ) { return UNKNOWN }
if  ( p.height < 60.0)  { return YES }
else { return NO }
}

Truth averageHeight(Person p) {
return ! ( isTall(p) || isShort(p) )
}

In the above code, the “averageHeight()” function returns a Truth value, and is completely defined by boolean NOT and the isShort() and isTall() functions, and it returns UNKNOWN if either of these functions is UNKNOWN.  The NOT (!) works properly now instead of the previous definition which mistakenly combined the “I can’t prove it” case with the “false” case.

Instead of a “if..then” statement in code, we can use a “switch” statement to handle YES, NO, UNKNOWN, and MU, like so:

switch(averageHeight(p) || isShort(p) ) {
case YES:
println "YES" ; break;
case NO:
println "NO" ; break;
case UNKNOWN:
println "UNKNOWN" ; break;
case MU:
println "MU" ; break;
}

We’d like to add a little DSL syntactic sugar to the switch statement, so the above could be written a bit more succinctly, something along the lines of:

/* idea for improvement to Truth DSL */
if (averageHeight(p) || isShort(p) ) {

YES: { println "YES" }
NO:  {println "NO" }
UNKNOWN: { println "UNKNOWN" }
MU: { println "MU" }
}

which would try to follow the pattern of if()…then()…else() but be: if…yes()..no()…unknown()…mu() with any of the blocks optional.

Please comment if you like this proposed addition to the DSL, or have any suggestions!

Feedback

I hope you have enjoyed learning about how Truth is implemented in the VDK to provide a richer logic representation than the Boolean True/False.

Please post any comments or questions in the comment section, or contact Vital AI directly at info@vital.ai

Running shell commands in Beaker Notebook

Data Science Notebooks like Beaker Notebook are a great way to not only explore and analyze data but also record the steps, so that the next Data Scientist can reproduce the results — just by clicking “Run”.

Few people like to spend time meticulously documenting their data analysis steps so to the degree that Data Science Notebooks can be “Self Documenting” — it greatly makes things a lot easier.

As Beaker Notebook can mix many programming languages within one Notebook like R, Python, and Groovy — most steps can be captured completely in a Notebook.

One case that is missing from Beaker however is the command line shell.  Bash is the default on Macintosh OSX, but the same is true for other shells, including the Windows shell or other Unix shells such as “csh” or “tcsh”.

Oftentimes shell commands are used for running data manipulation programs (like awk, perl, or sed), or running compiler processes (like maven or ant).

At Vital AI we use shell commands to run “vitalsigns” which compiles a data model into code, which is then used in data analysis, database queries, and machine learning processes (running inside Apache Spark).

It’s nice to run these within Beaker as not only a convenient way to avoid switching from Beaker to a terminal screen and back, but also to document these steps for reproducibility.

Fortunately with a little helper class it’s easy to run shell commands from Groovy cells in the Beaker Notebook.

The helper class is “RunBash.groovy” and is found on github here:
https://github.com/vital-ai/vital-data-utils/blob/master/src/main/groovy/ai/vital/data/utils/RunBash.groovy

Once a jar with this class is made available to Groovy via the Language Manager (see screenshot below), it can be used in a Groovy cell to run Bash scripts, like so:

import ai.vital.data.utils.RunBash

RunBash.enable() // hook .bash() to strings

//bash script begins here, in a Groovy multi-line string:
"""
echo \$VITAL_HOME

vitalsigns generate -o \${VITAL_HOME}/domain-ontology/vital-samples-0.1.0.owl -or
"""
.bash() // this runs the script</blockquote>

Here’s a screenshot of that running in Beaker:

runbash

Here’s a screenshot of the Language Manager (from the Notebook menu), with jars added to the Beaker Notebook classpath for Groovy.

beaker-languagemanager