## 14.1. The Advanced Inference Parameters

This section of the Handbook is devoted to the advanced inference parameters, a set of options that can be manipulated by users to change some of the behavior of the Cyc inference engine.

This section of the Handbook is devoted to the advanced inference parameters, a set of options that can be manipulated by users to change some of the behavior of the Cyc inference engine during backward inference (inference performed at ask time).

In order to see the advanced inference parameters, simply click on the [Show] button next to ‘Advanced Inference Parameters’ on the ‘Ask a Query’ page. After clicking on the button, you should see six inference parameters, each with a ‘Yes’ and ‘No’ option below it. You enable each of the inference parameters by choosing ‘Yes’, and disable each by choosing ‘No’. Each of the inference parameters is set to a default value: the default value for ‘Cache backward query results’ is ‘Yes’, while the default value for the other five parameters is ‘No’. I will now describe what happens when these parameters are enabled, and indicate why a user might want to enable them.

All parameters are set “no” by default.

### 14.1.1. ‘Enable HL predicate backchaining’

Enabling HL predicate backchaining allows the inference engine to backchain on rules in which a positive literal (that is, a clause in the consequent of a rule) has an HL predicate (that is, a predicate with its own dedicated HL module – #$isa, #$genls, #$elementOf, and #$subsetOf are notable examples) in its 0th argument place. An example of such a rule is the following:

BaseKB (implies (and (isa ?STYPE ExistingStuffType) (isa ?OBJ ?STYPE) (physicalDecompositions ?OBJ ?PORTION)) (isa ?PORTION ?STYPE))

When HL predicate backchaining is enabled, the inference engine will backchain on the above rule when a query of the form

(isa A B)

is asked (where ‘A’ and ‘B’ can be either closed terms or variables). On the other hand, when HL predicate backchaining is disabled, the inference engine will not backchain on the rule when given a query of the same form. Consequently, it is useful to enable HL predicate backchaining whenever one asks a query of the form

(PRED ARG1 ... ARGN)

where ‘PRED’ is an HL predicate, and ‘ARG1′, …, ‘ARGN’ are either closed terms or variables, and one anticipates proving the query (or finding bindings for the variables in the query) by backchaining on a rule containing a positive literal with ‘PRED’ in the 0th argument place.

One drawback to enabling HL predicate backchaining is that it increases the number of rules in the search space for a query, since rules with an HL predicate PRED in the 0th argument place of a positive literal would normally not appear in the search space when a query of the form

(PRED ARG1 ... ARGN)

is asked. So if you don’t anticipate that proving a query will require proving something of the above form (either as the final conclusion or as an intermediate conclusion in a series of backchaining steps) via backchaining on a rule with ‘PRED’ in the 0th argument place of a positive literal, it would probably be best to disable HL predicate backchaining, at least for that query.

### 14.1.2. ‘Enable unbound predicate rule backchaining’

This inference parameter is similar to ‘Enable HL predicate rule backchaining’ in that it also allows the user access to rules not usually used by the inference engine. Enabling unbound predicate rule backchaining allows the inference engine to backchain on rules in which a variable appears in the 0th argument place of a positive literal, rules like the following:

BaseKB (implies (and (hasRelationalAttributes ?DEP-THING ?BEINGINRELATION2WITH-ATTRIBUTEFN) (termOfUnit ?BEINGINRELATION2WITH-ATTRIBUTEFN (BeingInRelation2With-AttributeFn ?PRED ?INDEP-THING))) (?PRED ?INDEP-THING ?DEP-THING))

So when unbound predicate rule backchaining is enabled, the inference engine will be able to backchain on a rule like the one above in trying to prove (or find bindings for) a query of the form

(BINARYPREDICATE A B)

where ‘BINARYPREDICATE’ is a predicate, and ‘A’ and ‘B’ are either variables or closed terms. The advantages and drawbacks to enabling unbound predicate rule backchaining are similar to those associated with enabling HL predicate backchaining. Enabling unbound predicate rule backchaining will almost certainly increase the size of the search space for a given inference. On the one hand, enabling unbound rule predicate backchaining may be the only way one can prove a closed query, or get bindings for a query with one or more variables.

### 14.1.3. ‘Cache backward query results’

When the inference parameter ‘Cache backward query results’ is enabled, the results of successful inferences involving backchaining will be cached in the KB. So if a closed query (no free variables) of the form

(PRED ARG1 ... ARGN)

is asked, and the query returns ‘True’, the ground atomic formula (GAF)

(PRED ARG1 ... ARGN)

will be cached in the KB, in the microtheory in which the query was asked. Note that the cached assertion will have the direction

‘Backward’, so it won’t trigger any forward rules. If an open query (one with at least one free variable) of the form

(PRED ARG1 ... ARGN)

is asked (where at least one of the ARG1, …, ARGN is a free variable), and at least one set of bindings is returned as the result of the query, then each of the GAF’s obtained by substituting a set of bindings for the appropriate variables in the query will be cached in the KB. For instance, if one asks the query

(intends Iran (doneBy ?ACTION Iran))

in the AbuMusaIncidentMt, with ‘Cache backward query results’ enabled, 30 second time cutoff, and 1 backchain step, one should get several bindings for?ACTION,including

WarOfTheCities-IranianOffensiveIranOccupiesTumbIslands-1971IranReassertsSovereignty

Each of the GAF’s obtained by substituting one of these constants for?ACTIONin the query formula will be cached in the KB, in the query mt, with direction ‘Backward':

AbuMusaIncidentMt

(intends Iran (doneBy IranReassertsSovereignty Iran)) (intends Iran (doneBy IranOccupiesTumbIslands-1971 Iran)) (intends Iran (doneBy WarOfTheCities-IranianOffensive Iran))

Enabling ‘Cache backward query results’ can be very useful when one is testing out inferences involving backchaining on several rules: this one can do a separate query using one of the rules in the inference path, to cache a GAF or GAF’s that will be needed in one of the other backchaining steps. By caching these GAF’s, one reduces the number of backchaining steps needed for the query one is ultimately interested in testing out, and thus speeds up the process of seeing whether or not the query is provable via the chosen inference path.

It is often a good idea to disable ‘Cache backward query results’ when one is seeking to improve the speed of an inference involving backchaining. Trying to improve the speed of an inference often involves testing the same inference over and over again, to see if changes made in the KB have significantly cut the amount of time needed to get the correct answer to the query. If caching is enabled, then the results of the query one is running will be cached in the KB; consequently, these results can be found rapidly by the inference engine (via simple look-up modules) in subsequent runnings of the query. Consequently, one might be misled into thinking that the KB changes one made were significantly cutting the amount of time needed for an inference, when it was really the cached results of previous queries that were allowing the query to return significantly faster. For this reason, it is a good idea to disable caching when running the same query over and over again.

### 14.1.4. ‘Enable negation by failure’

Enabling negation by failure allows the inference engine to prove the negation of certain assertions when it fails to prove those assertions themselves.

By default, when negation by failure is off, Cyc does not employ the closed-world assumption in backward inference unless forced to do so via use of #$completeExtentKnown, #$completeExtentKnownForArg, or #$completeCollectionExtent. That is to say, in the default case, Cyc does not assume that it knows everything about every domain. Hence when one asks the negation of a closed formula FORM with negation by failure disabled, the inference engine will return ‘NIL’ if it cannot prove FORM. Because the closed world assumption is not enforced, the inference engine does not construe its own inability to prove FORM to be an argument for the truth of the negation of FORM.

When negation by failure is enabled, and one asks the negation of a closed formula FORM in which the arg0 is a predicate PRED such that (#$minimizeExtent PRED) is true in a microtheory accessible to the microtheory in which the query is made, then the inference engine will return ‘True’ if it cannot prove FORM. For example, if one enables negation by failure, and then asks

(not (hasMembers INTERPOL Watson))

in the CyclistsMt, the query will return ‘True’, since (hasMembers INTERPOL Watson) cannot be proven, and since

(minimizeExtent hasMembers)

is asserted in the InternationalOrganizationDataMt, a microtheory visible to the CyclistsMt. Note that the same query will return ‘Query was not proven’ when negation by failure is disabled. Note also that even when negation by failure is enabled, the query

(not (hasMembers INTERPOL UnitedStatesOfAmerica))

returns ‘Query was not proven’ when asked in the CIAWorldFactbook1995Mt, since the inference engine can prove

(hasMembers INTERPOL UnitedStatesOfAmerica)

in that microtheory, since

(internationalOrg-MemberCountry INTERPOL UnitedStatesOfAmerica)

is asserted there. Finally, it should be pointed out that enabling negation by failure can also affect inferences involving backchaining. For example, if one enables negation by failure, and then asks

(not (sponsorsAgentInAction Iran UnitedStatesOfAmerica RafsanjaniWarnsUAE))

in the AbuMusaIncidentMt, with 1 backchaining step, the query will return ‘True’. This is because the inference engine performs a kind of contrapositive reasoning on the rule

BaseKB (implies (sponsorsAgentInAction ?SPONSOR ?DOER ?ACT) (performedBy ?ACT ?DOER))

reducing the problem of proving

(not (sponsorsAgentInAction Iran UnitedStatesOfAmerica RafsanjaniWarnsUAE))

to that of proving

(not (performedBy RafsanjaniWarnsUAE UnitedStatesOfAmerica))

Since negation by failure is enabled, and since the assertion

(minimizeExtent performedBy)

is asserted in the BaseKB, the negated performedBy literal can be proven.

Since negation by failure allows us to assume that the negation of an assertion is true when the assertion itself cannot be proven, it is best used in those situations in which such an assumption is plausible, or, alternatively, in situations in which one wishes to test the plausibility of such an assumption.

### 14.1.5. ‘Consider disjunctive temporal relations’

Enabling ‘Consider disjunctive temporal relations’ allows the SBHL-TIME module to use certain assertions in the KB that it would normally not use. The assertions in question are either ground atomic formulas (GAFs) in which temporallyDisjoint is the arg0, or negated

GAFs in which the arg0 of the negated GAF is one of the following predicates:

temporallySubsumestemporalBoundsContainstartingDateendingDatedateOfEventcontiguousAftertemporallyFinishedBytemporalBoundsIntersecttemporallyIntersectstemporallyCoterminaltemporallyCooriginatingtemporalBoundsIdenticaltemporallyStartedBycotemporaloverlapsStartendsDuringstartsDuringdateOfDeathbirthDate

Assertions of the form mentioned above are disjunctive in the sense that each of them encodes information that is equivalent to a disjunction of two or more temporal relations holding between the arguments of the assertion. For example, the assertion

(temporallyDisjoint BritneySpears Trotsky)

is equivalent to the disjunction

(or (startsAfterEndingOf BritneySpears Trotsky) (startsAfterEndingOf Trotsky BritneySpears))

Enabling ‘Consider disjunctive temporal relations’ adds some time to queries involving temporal relations, and that is why the default value of ‘Consider disjunctive temporal relations’ is ‘No’. However, the amount of time that is added to queries is often negligible, so OE’ers should feel free to enable this option, if they think that their queries will involve the use of assertions of the form mentioned above.

### 14.1.6. ‘Semantic pruning of results of backchaining’

If you enable ‘Semantic pruning of results of backchaining’, then during inferences involving backchaining, certain nodes in the search tree will be subjected to a semantic well-formedness test. If the nodes fail that test, then they will be immediately pruned from the search tree. The test is applied whenever backchaining introduces #$isa or #$genls literals; when such literals are introduced, they are tested to see if they are provably unsatisfiable. If they are provably unsatisfiable, then the node at which the backchaining step was introduced is immediately removed from the search tree.

In order to get an idea of what happens when this inference parameter is enabled, ask the following query in the CurrentWorldDataCollectorMt, with a 40 second Time Cutoff and 1 backchaining step:

(performedBy ?ACTION Iran)

When asked with ‘Semantic pruning of results of backchaining’ disabled, the query should return three bindings for ‘?ACTION’, with the message ‘Search space exhausted’. If you go to the ‘Inference Tree Examiner’ page, you should see that there are 535 nodes in the search tree. Moreover, the top search node has 167 children.

When the same query is asked with ‘Semantic pruning of results of backchaining’ enabled, the query should return the same three bindings with the same message. However, when you go to the ‘Inference Tree Examiner’ page, you will find that there are only 492 nodes in the search tree, and that the top search node has only 124 children. The difference in the total number of nodes (and the difference in the total number of children for the top search node) is due to the results of semantic pruning. For instance, rules like the following are children of the top search node in the inference done with semantic pruning disabled:

UnitedStatesSocialLifeMt (implies (and (isa ?PERSON (GraduateFn LawSchool)) (termOfUnit ?ATTENDING (SKF-57340835 ?PERSON))) (performedBy ?ATTENDING ?PERSON))

HumanSocialLifeMt (implies (and (isa ?S Survivalist) (termOfUnit ?STORING (SKF-3782658 ?S))) (performedBy ?STORING ?S))

These rules do not appear in the search tree for the inference in which semantic pruning was enabled. They were pruned from that search tree because (isa Iran (GraduateFn LawSchool)) and (isa Iran Survivalist) are provably unsatisfiable.

The preceding example illustrates how enabling semantic pruning can appreciably reduce the number of nodes searched, even in a rather simple one backchain inference. Note that applying the semantic well-formedness test to #$isa and #$genls literals does take time; in fact, the gain in time that one gets from having a truncated search tree may very well be offset by the amount of time lost doing the test. Nevertheless, it’s often worthwhile to at least try out semantic pruning, particularly on inferences involving a number of backchaining steps.

## 14.2. Proof Checker Mode

In this section of the OE Handbook we describe the use of the proof checker, a tool that allows users to choose the rules they will use in querying the Knowledge Base.

In order to choose a rule for use by the proof checker, first click on the colored ball next to that rule in the browser interface. This will take you to a page that gives you a list of operations (such as Edit, Unassert, and Blast) that can be performed on the assertion. Here is an example of such a page:

Public Cyc Assertion 128400 [Show English] [EL Formula] [Diagnose] [HL Data] [Change Mt] [Change Strength] [Change Direction] [Assert Similar] [Edit] [Unassert] [Blast] [Use in Proof] Strength : Default Direction : Backward Arguments : 1 No Dependents Asserted locally by William Jarrold on Apr 24, 1996 Mt : BaseKB HL Formula : M(implies (and (isa ?ANIM Animal) (providerOfMotiveForce ?ACT ?ANIM)) (doneBy ?ACT ?ANIM))

One of the options at the top of the page is [Use in Proof]. Selecting this option adds the rule to the set of rules in the proof checker. After adding all the rules you wish to add to the proof checker, you can enable proof checking by first clicking on the [Show] button next to ‘Advanced Inference Parameters’ on the ‘Ask a Query’ page. After clicking on the [Show] button and scrolling down the page, you should see a ‘Proof Checker Setup’ link. Clicking on this link takes you to a page with ‘Proof Checker Control’ at the top. All the rules you have chosen for the proof checker should be listed on this page, and there should be three buttons, one saying ‘Enable Proof Checking’, another saying ‘Clear Entire Rule Set’, and a third saying ‘Update Rule Set’. To enable proof checking, simply press the ‘Enable Proof Checking’ button. After proof checking has been enabled, a link ‘Proof Checking mode Enabled’ should appear just below the ‘Ask Query’ button on the ‘Ask a Query’ page.

As long as proof checking mode is enabled, the only rules that will be used in backchaining are those rules that the user has chosen for the proof checker. So suppose that the rule mentioned above is the only rule chosen for the proof checker, and that proof checking has been enabled. Under these circumstances, the only rule that would appear in the search tree for the query

(doneBy ?X ?Y)

in the #$HumanSocialLifeMt, with 1 backchain step, would be the rule mentioned above. If the same query were asked with proof checking disabled, a far greater number of rules (48, when I asked) would appear in the search tree. Consequently, enabling proof checking mode allows one to shrink the search space to a small number of rules (namely, all those rules placed in the proof checker). Shrinking the search space to just the rules placed in the proof checker allows one to determine quickly whether or not an inference involving those rules (even one that requires several backchaining steps) will be successful. Consequently, the proof checker is a useful tool for debugging potential inference paths.

Once you are through using the proof checker, you can disable proof checking simply by clicking on the ‘Disable Proof Checking’ button on the ‘Proof Checker Control Page’ (which can be reached by clicking on the ‘Proof Checker Setup’ link on the ‘Ask a Query’ page).

## 14.3. Inference Sensitive Predicates

This section of the OE Handbook will focus on the collection of CycInferenceHeuristicPredicates, and how they can be used by OE’ers to modify how the inference engine behaves during a query.

The collection of #$CycInferenceHeuristicPredicates includes predicates like #$highlyRelevantAssertion, #$highlyRelevantMt, and #$backchainForbidden. Through the use of these predicates, an OE’er can modify the heuristic search mechanisms of the inference engine for certain types of queries. We will now illustrate the advantages and drawbacks of these predicates with a few examples.

By asserting

(backchainForbidden PRED)

in a microtheory MT, one places restrictions on backchaining on rules containing a positive literal with PRED as the arg0, whenever a query is done in a microtheory having access to MT. For instance,

(backchainForbidden inRegion)

is asserted in the #$TourAndVacationPackageItinerariesMt. Consequently, whenever a query is asked in a microtheory having access to the #$TourAndVacationPackageItinerariesMt, backchaining on rules containing a positive literal with inRegion as the arg0, like

BaseKB (implies (and (inRegion ?OBJ ?SUB) (geographicalSubRegions ?REGION ?SUB)) (inRegion ?OBJ ?REGION))

will be restricted. To be more specific, whenever a query of the form

(inRegion A B)

is asked in a microtheory having access to the #$TourAndVacationPackageItinerariesMt (where ‘A’ and ‘B’ could be either closed terms or variables), backchaining on the rules like the one above (that is, rules containing a positive literal with inRegion as the arg0) cannot be used to prove the query. More generally, if

(backchainForbidden PRED)

is asserted in a microtheory MT, then queries of the form

(PRED ARG1 ... ARGN)

(where ‘ARG1′, …, ‘ARGN’ could be either closed terms or variables), when asked in a microtheory having access to MT, cannot be proven by backchaining on rules containing a positive literal with PRED as the arg0.

At first glance, it may be difficult to see the utility of asserting

(backchainForbidden PRED)

since all that making such an assertion seems to do is to take away some resources (namely, certain backward rules) that might be useful in proving queries of the form

(PRED ARG1 ... ARGN)

However, asserting

(backchainForbidden PRED)

in a microtheory MT can in fact be of great utility, if two conditions are met. First, microtheories that have access to MT (including MT itself) should be contexts in which we would not expect to prove many (if any) queries of the form

(PRED ARG1 ... ARGN)

via backchaining. Second, the microtheory MT should be one with access to a fairly large number of rules containing a positive literal with PRED as the arg0. The first condition ensures that nothing will be lost by restricting backchaining, while the second condition ensures that something will be gained. What will be gained is a speed-up in inference, since the inference engine will not have to consider rules containing a positive literal with PRED as the arg0 when trying to prove a literal of the form

(PRED ARG1 ... ARGN)

Note that finding microtheories that meet the two conditions above can often be a delicate matter, and so assertions of the form

(backchainForbidden PRED)

should be made with caution. Testing the consequences of such assertions by asking several queries is thus highly encouraged.

By asserting

(backchainRequired PRED)

in a microtheory MT, one places restrictions on the use of removal modules to prove literals of the form

(PRED ARG1 ... ARGN)

To be more specific, if one asserts

(backchainRequired PRED)

in a microtheory MT, then the inference engine will only attempt to use transformation HL modules (roughly, backchaining modules) on literals involving PRED, when a query is made in a microtheory having access to MT. The inference engine will prune any inference path in which a removal module would need to be attempted on such a literal.

So backchainRequired is a kind of dual to #$backchainForbidden; the former rules out the use of removal modules to prove literals of a certain kind, but allows the use of transformation modules to prove those literals, while the latter rules out the use of transformation modules to prove certain literals, but allows the use of removal modules.

Note that the use of #$backchainRequired should be limited to those contexts in which it makes sense to think that literals involving a predicate should only be proved via backchaining.

The predicates #$highlyRelevantAssertion and #$highlyRelevantMt can be used to modify the heuristic weight given to an assertion or assertions in certain inferences. When one asserts

(highlyRelevantAssertion ASSERT)

in a microtheory MT, the #$CycLAssertion ASSERT will be given greater heuristic weight than it normally would in inferences done in MT. As a consequence, ASSERT will most likely be used at a much earlier stage in queries done in MT than in queries done in microtheories where ASSERT is not declared to be a #$highlyRelevantAssertion. Since ASSERT will most likely be used at a much earlier stage in such queries, queries that successfully use ASSERT can usually be run in a much shorter time in MT.

Asserting

(highlyRelevantMt MT)

in a microtheory MT-1 (where MT-1 need not be the same as MT) has the effect of making each of the assertions in MT a #$highlyRelevantAssertion for inferences done in MT-1.

Note that in some cases, asserting

(highlyRelevantAssertion ASSERT)

or

(highlyRelevantMt MT)

in a microtheory MT-1 may not have the effect of speeding up an inference asked in MT-1, even if ASSERT (respectively, the assertions in MT) are successfully used in that inference. Most notably, if the query involved is an exhaustive ask (one where the ‘Number Cutoff’ option chosen is ‘Get Everything’, and one in which the query contains some open variables), there will be no speed-up in inference, since the inference engine will continue to search for variable bindings until the search space is exhausted. Even if well-placed #$highlyRelevantAssertion or #$highlyRelevantMt GAF’s allow the inference engine to find all the bindings it will find in a search within the first ten seconds of that search, the search will continue until the search space is exhausted. So in order to get the most out of the predicates #$highlyRelevantAssertion and #$highlyRelevantMt, one should avoid exhaustive asks; the best way to do this is by imposing a number cutoff other than ‘Get Everything’.

The other instances of #$CycInferenceHeuristicPredicate – #$irrelevantMt, #$irrelevantAssertion, #$irrelevantPredAssertion, #$backchainDiscouraged, and #$backchainEncouraged – are not currently supported in code, and thus won’t be discussed here.

## 14.4. Theorem Proving vs. HL Modules

### 14.4.1. Overview

It’s important for OEers to understand how the inference engine works, so that they can write CycL axioms that can be used most efficiently in inference. An important distinction in the inference engine is the one between theorem proving and HL modules.

The two main steps of inference are transformation and removal. “Removal” is an inference step which strictly simplifies the problem. It removes (i.e. solves, generates bindings for) one of the literals in the subquery it’s considering. “Transformation” is an inference step which does not strictly simplify the problem; instead it transforms the problem into a new problem. The typical example of transformation is backchaining. Removal strictly simplifies the problem; transformation may complicate it. Hence, the number of transformation steps allowed plays a large part in the size of the proof space that will be explored. Since the most common type of transformation is backchaining (see “Current HL Modules”), the terms “transformation” and “backchaining” are often used interchangeably, which is technically incorrect.

### 14.4.2. Defining New Predicates

Backchaining is what makes rules work. Say that you’ve just created a new predicate, #$pointWithinRectangle, which takes a 2-D point as an arg1, and a 2-D rectangle as an arg2. Just to make the example simpler, let’s assume that rectangles cannot be tilted with respect to the Cartesian plane. There are two approaches to making #$pointWithinRectangle literals provable in inference.

#### 14.4.2.a. You could define the meaning of #$pointWithinRectangle by rules.

For example, (making up some predicates on the fly here for pedagogical purposes, and assuming that coordinates are represented by real numbers):

(#$implies (#$and (#$minXCoordOfRectangle ?RECT ?MIN-X) (#$maxXCoordOfRectangle ?RECT ?MAX-X) (#$xCoordOfPoint ?POINT ?POINT-X) (#$lessThan ?MIN-X ?POINT-X) (#$lessThan ?POINT-X ?MAX-X) (#$minYCoordOfRectangle ?RECT ?MIN-Y) (#$maxYCoordOfRectangle ?RECT ?MAX-Y) (#$yCoordOfPoint ?POINT ?POINT-Y) (#$lessThan ?MIN-Y ?POINT-Y) (#$lessThan ?POINT-Y ?MAX-Y)) (#$pointWithinRectangle ?POINT ?RECT))

The above rule could be usefully used in inference, with one backchain on #$pointWithinRectangle. Any time that the inference engine tries to prove a #$pointWithinRectangle literal and it is not already immediately known, then it could use the above rule to transform the #$pointWithinRectangle literal into the ten conjuncts in the antecedent of the above rule, and if all ten conjuncts can be proven, then the #$pointWithinRectangle literal can be proven.

However, what if you wanted to extend this to handle rectangles which were tilted with respect to the Cartesian plane? It would be quite challenging to come up with rules that defined such a predicate accurately, and it would probably be impossible to do it both accurately and efficiently.

The advantages of the rule-based approach are that it is modular, explanatory, and you don’t have to be a programmer to implement it. The rule-based approach will work for most problems in ontological engineering. However, when you’re working with anything math-heavy or anything which could be solved with a computational algorithm simpler than arbitrary theorem proving, then you might want to consider an HL module.

#### 14.4.2.b. You could define the meaning of #$pointWithinRectangle via EL methods, and use an HL-module to give this definition utility in inference.

By writing code to specially handle proving #$pointWithinRectangle literals, you can obviate the need for rules at all, and use whatever mathematical or computational tools you wish to prove the literal in code.

A disadvantage of this approach is that it is more opaque to ontological engineers; it is not always obvious how the system concluded the truth or falsity of a particular literal. Often it bottoms out in “Because this particular piece of code was evaluated, and it said so.” Writers of HL modules can mitigate this problem by including useful and explanatory supports, often in the form of “code rules” (rules with direction :code), in the results returned by their HL modules.

### 14.4.3. Taking Advantage of Existing HL-supported Predicates

Even more important than knowing the advantages and disadvantages of theorem proving vs. HL modules when defining new predicates is taking advantage of the existing HL support when making new assertions in Cyc.

For instance, an OEer might write a rule like the following:

(#$implies (#$and (#$relationAllExists ?PRED ?ALL-COL ?EXIST-COL) (#$genls ?ALL-SPEC-COL ?ALL-COL)) (#$relationAllExists ?PRED ?ALL-SPEC-COL ?EXIST-COL))

So that if Cyc knew, for example, that all dogs have tails, then all poodles must also have tails. However, the above rule can be replaced by the following gaf:

(transitiveViaArgInverse relationAllExists genls 2)

which has the same meaning. Without the HL-support for #$transitiveViaArg (or something similar), in order to derive

(relationAllExists anatomicalParts Poodle Tail-BodyPart)

from

(relationAllExists anatomicalParts Dog Tail-BodyPart)

you would need to backchain one step on the above rule. With the HL-support for #$transitiveViaArg (and the GAF listed above), you can ask

(relationAllExists anatomicalParts Poodle Tail-BodyPart)

with 0 backchain steps and get “True” as a result.

It is a good idea for ontological engineers to become familar with what predicates have HL-support in order to best be able to anticipate the behavior of the inference engine, thus writing the most efficient axioms on constants in order to take advantage of such predicates.

## 14.5. Inference Tree Examiner

### 14.5.1. Purpose

The Inference Tree Examiner is a debugging tool which allows one to browse the internal datastructures of an inference for a particular query. The tool shows things like:

- all proofs pursued in the inference
- the proofs which have succeeded so far
- dead-end proofs, and the reason they were pruned
- the sequence of deductions used in each proof
- the intermediate steps of each proof
- the inference methods used at each step
- the bookkeeping maintained during the proof

Consequently, this is the primary tool for debugging both the OE used in inferences, and the inference mechanism itself.

### 14.5.2. Inference Trees

Since the Inference Tree Examiner is simply a browser for surfing around the datastructures used in an inference, it is worth providing a brief overview of these datastructures and the inference process that manipulates them.

Inference in Cyc is modelled as a search through proof-space for unique deductive proofs that justify answers for a given query. A large number of special-case inference methods called HL modules provide the means for making each of the steps in a proof.

The main datastructure involved is an inference search tree, which stores the current state of the search in progress. It is a set of search nodes arranged as a tree. Each search node represents a sub-query to prove. Consequently, each node is an intermediate state of the inference search being pursued down a particular proof path. Since the nodes are arranged as a tree :

- every search node has exactly one parent node
- except for the root(s) of the tree, which has no parent

#### 14.5.2.a. Root nodes & Leaf nodes

The root of the tree represents the query which was actually asked, and thus is the starting point for pursuing proofs. Most searches have a single root; disjunctive searches typically have one root for each disjunct.

Leaf nodes (nodes with no children) are the duals of root nodes (nodes with no parent), and represent the ending point for a potential proof.

#### 14.5.2.b. Child nodes of a node

The child nodes of each search node represent unique sub-problems introduced by a deductive inference step by an application of an HL module. In other words, if the child node’s sub-problem generates an answer, then that answer, combined with the inference step used to go from the search node to the child node, together constitute an answer for the search node.

#### 14.5.2.c. Goal nodes

A goal node is a leaf node of the inference tree in which the sub-problem to prove is #$True. The path from a goal node all the way up to a root constitutes one unique proof of one unique answer for a query.

Thus, the objective of inference is essentially to construct as many goal nodes as efficiently as possible.

Not all leaf nodes are goal nodes. Some represent dead-ends, where we’ve identified something in the intermediate sub-problem for which we know we can’t generate any answers. The remaining leaf nodes represent sub-problems which are still being worked on, and may yet result in more child nodes.

The Inference Tree Examiner focuses on the search nodes of the inference, and allows browsing up and down the parent/child hierarchy of the search tree they constitute.

### 14.5.3. Access

The HTML interface remembers the inference datastructures for the last query you performed via the ASK page, and allows you to invoke the Inference Tree Examiner on it via links on the ASK page.

The link

Examine previous inference ...

allows you to browse the inference for the most recent query performed in the interface.

Also, if the ASK page has the results of a query displayed, the reason shown for why that query halted is also a link to browse the inference. For example :

Query halted because : Number cutoff was reached.

In both these cases, the link takes you to the root node of the search tree.

### 14.5.4. General Layout

The page for a search node has 4 main sections, some of which only appear for certain nodes or in certain cases, and are shown in the following order :

- Search Roots (optional)This section only appears if there is more than one search root, and it simply shows a list of each of the roots.
- Node SectionThis section shows all the information about the node itself, including the Current Query State. If it is not a top node, it shows the method and supports used to transform its parent into itself, and the bookkeeping information associated with it.
- Ancestors Section (optional)This section only appears if the node is not a root node, and simply shows the complete sequence of ancestor search nodes upwards from its parent to its root node.
- Children Section (optional)This section only appears if the node has at least one child node. It shows the immediate children of the search node. The child nodes are sorted by node id, with all nodes that have some goal descendant show before all those without.

### 14.5.5. Specific Features

Some of the more specific features of the interface will now be described in more detail.

Links to search nodes are displayed in one of these two formats :

- T(D,ID(Q))
- R(D,ID)

Key :

T- a node for which transformations are still possible
R- a node for which only removals are still possible
D- the depth of the search node
ID- the id of the search node
Q- the heuristic transformation quality of the search node

If the link has no remaining options, it is surrounded by square brackets.

Node- This is the current node being displayed, so it is basically a refresh link.
Parent- This is the parent node of this node.
Node N out of M in search number K

K- the search number of this search, which is the K’th search that this image has performed.
M- the current number of search nodes in the search.
N- the node number of this node, which is the N’th search node introduced so far in this search.
Depth- This is the total depth of the current node in the tree. It represents the number of inference steps used so far to get down to this node from a root node.
Transformation Depth- This is the transformation depth of the current node in the tree. It represents the number of transformation (backchain) steps used so far to get down to this node from a root node.
Remaining Options- This represents the inference options still available at this search node.”Options are Undetermined” indicates that the search node has not yet even been examined to compute what its inference expansion options are.
“No Remaining Options” indicates that the search node has had all its options determined and completely expanded. There is no possibility for any further direct children of this node.

Quality- This is number representing the heuristic transformation quality of this node. Larger values indicate a node which is deemed more promising for further transformation.
HL Module Used- This shows the HL module which was used to produce this search node from its parent node.
Parent Literal Removed- This shows the literal in the parent query state which was removed by the HL module in order to produce this search node. In other words, this is what in the parent was conditionally proven by the HL module, resulting in this node’s current state.
Support Used- This shows the inference support used by the HL module to justify producing this search node from the parent node.
Additional Supports- If present, this shows the list of any additional inference supports used by the HL module to justify producing this search node from the parent node.
Free Variables- Shown only for a root node, this indicates the EL variables in the query which are free variables.
Bindings Established- This shows the mapping between the HL variables in the parent node, and what they got bound to in the current node’s state.For a root node, a list of the EL variables used for the HL variables in the node’s state are shown.
Current Query State- This shows the CycL query for the sub-problem represented by this search node. It represents what still needs to be proven down this particular proof path.”Goal!” indicates that the CycL query is #$True
If a literal is listed in BOLD, it means that transformation (backchaining) is still potentially an option for that literal.

Unsatisfiable Literal- For a dead-end leaf node, this shows the literal in the query state which resulted in there being no child nodes. In other words, this was the literal which allowed the inference engine to prune this search, because no way to prove it (and thus the entire sub-problem) is available.

### 14.5.6. Additional Tools

In addition to browsing the search nodes of the inference tree, there are some additional tools available

[Continue Ask]- This allows for continuing the current query with additional resources.
[Socratic Ask]- This allows for invoking a new query where the formula is the current state of this node.
[Goal Descendants]- This shows a page which lists all of the currently identified goal nodes that are descendants of the current node.

### 14.5.7. Suggested Uses

The most common use of the Inference Tree Examiner is to just browse the tree and see what supports got used in the proof process. You can follow the paths you think look promising and see where they dead-end, and the unsatisfiable literals which led to the dead-ends.

The [Goal Descendants] tool is very useful for going straight to all the successful goal nodes that lie underneath some ancestor node.

When attempting to debug an inference that seems to dead-end, [Socratic Ask] is very helpful to identify a sub-problem which should be solvable, and starting a new query from that exact point.

### 14.5.8. Proof Checker

One of the most powerful uses of the Inference Tree Examiner is to perform inferences in Proof Checker mode. In this mode, the only rules which are available for backchaining are specific rules that the user identifies. This is extremely useful for efficiently debugging inference paths that use rules by focusing inference only on a set of rules that you want considered.

To use Proof Checker mode, you must first identify a set of rules for the proof checker to use.

To identify a rule you want to use in the Proof Checker, you should click on

[Use in Proof]

from the assertion display page.

To enable or disable Proof Checker mode, click on

Proof Checker Setup

under the Advanced Inference Parameters section on the Ask page. This takes you to the Proof Checker Control page, where you you can also remove some or all rules from the rule set, as well as toggle proof checking on and off.

When the Proof Checker is enabled, the Ask page will display

Proof Checking mode Enabled

and, while enabled, all proofs that use any rule not in the proof checker set are immediately pruned from the search.

Please see the section on “Proof Checker Mode” for more information.

### 14.5.9. Past & Future

The Inference Tree Examiner originated as a tool for the inference developers to debug the inference code. Relatively little time or effort has been devoted to its development since its initial motivation. As such, it currently shows lots of bookkeeping arcana which may or may not be relevant to its other uses.

Our goal is to extend it to be more useful for OE debugging, so any ideas for improvement are welcome.

## 14.6. Negation by Failure

*This section is not yet available. *

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