CN110069747A - Ontology logical contradiction processing method based on integral linear programming - Google Patents
Ontology logical contradiction processing method based on integral linear programming Download PDFInfo
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Abstract
The present invention discloses a kind of based on integral linear programming (Integer Linear Programming, ILP the method for logical contradiction in ontology) is solved, give the ILP model for solving logical contradiction, it is indicated by the way that given conflict set is changed into ILP, and then obtains best solution using traditional ILP solver.The corresponding axiomatic set theory of each scheme, gathers as removal one from ontology, can solve given conflict.Present invention firstly provides the algorithms of a calculating basis minimal solution, so that the axiom deleted is as few as possible, it is also proposed that retain the algorithm of weight informations as more as possible.The method proposed by the present invention for solving conflict based on ILP is a general logical contradiction processing method, can be not only used for repairing single ontology and Ontology Mapping, can be also used for doing ontology amendment or Ontology Evolution.The present invention illustrates that the algorithm proposed has very high efficiency by experiment abundant, and the axiom deleted has radix minimum or weight and the smallest property.
Description
Technical field
The invention belongs to the inconsistent processing technology fields of ontology logic in semantic net, are related to a kind of from given conflict set
Remove the method for lacking axiom as far as possible, specially a kind of ontology logical contradiction processing method based on integral linear programming.
Background technique
In semantic net (Semantic Web), ontology (ontologies) is played the part of emphatically as the representation of knowledge of formalization
The role wanted.Since building ontology is being very easy to error of the task, and ontology always ceaselessly varies, therefore
Ontological construction, ontology amendment (ontology revision), Ontology Mapping (ontology mapping) and Ontology Evolution
Inevitably there is logical contradiction (logical in many application scenarios such as (ontology evolution)
contradictions).In general, logical contradiction is divided into inconsistent (inconsistency) and uncoordinated
(incoherence).If an ontology does not have any model, this ontology is inconsistent；If deposited in an ontology
The concept of empty set is construed at one, then the ontology is referred to as uncoordinated ontology, which, which is referred to as, can not meet concept
(unsatisfiable concept).Under normal conditions, it in the uncoordinated term for tending to occur at ontology, and is not assisted to one
The example for adjusting ontology addition concept or relationship is easy to cause ontology to become inconsistent.It is pushed away due to carrying out standard for inconsistent body
Reason can derive any conclusion, so that these conclusions lose meaning, so solving logical contradiction is one both intentional
Adopted and important task.
When solving logical contradiction, people always it is expected to remove least axiom, i.e. solution should meet minimum change
Change principle.For this purpose, most of existing method touches Ji Shu (Hitting Set Tree, HST) algorithm using Reiter.
Schlobach etc. and the researchers such as Du propose to meet in minimum and keep finding out a minimum using HST algorithm in subset
Axiom collection delete, restore the harmony of ontology；Du etc. proposes to handle this using HST algorithm in minimum inconsistent subset again
The inconsistency of body；Kalyanpur etc. has modified HST algorithm, and weight is added in each edge for touch Ji Shu, is deleted with this to calculate
Except the smallest axiom collection of cost.Although these algorithms can find the minimum axiom collection or the smallest axiom of weight for deletion
Collection, but when Peng Jishuzhong branch is more, the algorithm based on HST is still very time-consuming.
In order to improve the efficiency for the method for solving logical contradiction based on HST, researchers' proposition is some can to reduce search
Space is able to satisfy the algorithm that certain minimum change defines again.For example, the propositions such as Qi first extract a subset from each conflict, so
HST algorithm is applied in these subsets afterwards, greatly increases efficiency in this way.There are two ways to selected subset, one is
It is that each axiom is given a mark in conflict set according to scoring functions, those highest public affairs of giving a mark then is chosen from each conflict
Reason；Another kind is the weight according to axiom, and the minimum axiom of weight is selected from each conflict.However, when the subset picked out
When also including more axiom, the efficiency of such methods is still problem, and cannot be guaranteed the axiom collection found for it is entire this
Body is the smallest.
In order to further increase the efficiency of logical contradiction processing, people have also been proposed didactic method, thoroughly abandon most
The principle of small variation.The it is proposed such as Schlobach is deleted according to axiom score, and score highest is first deleted from all conflict sets
That axiom, then delete the highest axiom of present score again from the remaining conflict set for not removing any axiom, so
Circulation is gone down, until there is axiom to be removed in all conflict sets.Also some works that logical contradiction is handled in body learning
Make, especially iteratively learns ontology, the method for most common processing logical contradiction is: for each axiom newly acquired, such as
Fruit adds the axiom and original ontology is made to become inconsistent or uncoordinated, then directly abandons the axiom.
To sum up, often give up efficiency in current logical contradiction solution in order to meet minimum change, or
Person gives up minimum change for efficiency, lacks very much the method for being suitble to any ontology that the two is taken into account, more lacks calculating basis
The method of the smallest axiom collection.In view of integral linear programming be often used in solve in the case where meeting certain restraint condition minimize or most
The problem of linear objective function of bigization, and our Solve problems are that axiom as few as possible is deleted from conflict set, two
Person is similar, therefore we carry out logical contradiction solution using 0-1ILP (hereinafter referred to as ILP) model.
ILP problem be for given several Boolean variables and some linear restrictions, calculate meet it is all to concludeing a contract or treaty
The resulting variable of a linear objective function is minimized or maximized in the case where beam to assign, the value of each variable can only
It is 1 or 0.There are many applications in semantic net field based on the model of ILP, Straccia and Bobillo apply it
To in fuzzy ontology reasoning (fuzzy ontology reasoning), it is applied to ontology by Niepert and Noessner etc.
In mapping tasks, it is used knowledge base and filled up in the work of (knowledge base completion) by Wang and Guo etc..
It is effective when reply has Complex Constraints problem that these applications all demonstrate the model based on ILP, and has very high
Efficiency.
Summary of the invention
In response to the problems existing in the prior art, the purpose of the present invention is to provide a kind of ontologies based on integral linear programming to patrol
Collect contradiction processing method.This method calls traditional ILP solver to obtain one by indicating logical contradiction with ILP model
It is best to assign, then the appointment is converted into an axiom collection, the axiom of axiom concentration is removed from ontology, can solve to give
Logical contradiction.
To achieve the above object, the technical solution adopted by the present invention is that:
Ontology logical contradiction processing method based on integral linear programming, comprising the following steps:
Step 1, the source for providing ontology；
Step 2 calculates conflict by ontology debugging tool, and to each conflict calculating and setting time that can not meet concept
Threshold value；
Step 3 constructs objective function according to practical application, and is constructed and constrained according to each conflict；
Step 4 calls existing integral linear programming solver to be solved, and obtain first variable is assigned conduct
Output；
Step 5, the solution for assigning building final according to the variable that solver returns, are deleted in the program from ontology
Axiom can solve given logical contradiction.
Preferably, step 1 further comprises: selecting from existing ontology library or constructs one by ontology construction tool and does not assist
Ontology O is adjusted, concept can not completely or partially be met by then therefrom selecting.
Preferably, step 2 further comprises: minimal conflict sets is calculated using ontology debugging tool, if calculating one
The conflict set of concept exceeds schedule time, then stops by force, retains the conflict found.
Preferably, step 3 further comprises: all conflicts found being merged in a set CONF, for the punching
Prominent collection carries out model construction.
The step of carrying out model construction preferably for the conflict set in step 3 further comprises:
Step 3-1, all different axioms in conflict set are obtained, set S is constitutedunion；
It step 3-2, is set SunionIn each axiom construct a binary variable, obtain binary variable set X, in this way
Variable can only value 0 or 1；
Step 3-3, construct optimization object function Z: when thinking that each axiom is of equal importance, objective function is institute in X
There is the sum of variable；When considering weight, objective function is the sum of the weighting of all variables in X；
Step 3-4, for each conflict conf in CONF, a constraint condition, i.e. each axiom pair in conf are constructed
The sum of variable answered is more than or equal to 1, it can thus be concluded that constraint set C.
Preferably, step 4 further comprises: calling existing ILP solver, asks in the case where meeting and constraining set C
The variable obtained when solving the minimum value of objective function Z assigns Sassi。
Preferably, the ILP solver called in step 4 includes CPlex.
Preferably, step 5 further comprises: according to SassiFinal solution is constructed, i.e. acquisition SassiIntermediate value is 1
The corresponding axiom of variable, the set of these axioms are exactly the scheme for solving given conflict CONF.
Compared with prior art, the beneficial effects of the present invention are:
(1) present invention proposes a general ontology logical contradiction processing method based on ILP, can be not only used for repairing
Single ontology and Ontology Mapping can be also used for doing ontology amendment or Ontology Evolution；
(2) the invention proposes one it is efficient, can be with the logical contradiction Processing Algorithm of calculating basis minimal solution；
(3) the invention proposes a logical contradiction processing that is efficient, can calculating weight and minimal solution to calculate
Method.
Detailed description of the invention
Fig. 1 is the schematic diagram of solution logical contradiction main process according to an embodiment of the present invention；
Fig. 2 is according to an embodiment of the present invention for the ontology meter with different number conflict (conflict size is 3)
Calculate the schematic diagram the time required to a solution；
Fig. 3 is according to an embodiment of the present invention for the ontology meter with different number conflict (conflict size is 4)
Calculate the schematic diagram the time required to a solution；
Fig. 4 is according to an embodiment of the present invention for the ontology meter with different number conflict (conflict size is 5)
Calculate the schematic diagram the time required to a solution.
Specific embodiment
Below in conjunction with the attached drawing in the present invention, technical solution of the present invention is clearly and completely described, it is clear that
Described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on the implementation in the present invention
Example, those of ordinary skill in the art's all other embodiment obtained under the conditions of not making creative work belong to
The scope of protection of the invention.
The present invention provides a kind of ontology logical contradiction processing method based on integral linear programming, and this method is not only efficiently but also full
Sufficient minimum change principle comprising following steps:
Step 1, the source for providing ontology；It is selected from existing ontology library or uncoordinated by ontology construction tool building one
Ontology O, concept can not completely or partially be met by then therefrom selecting.
Step 2 calculates conflict by ontology debugging tool, and to each conflict calculating and setting time that can not meet concept
Threshold value；Minimal conflict sets are calculated using ontology debugging tool, if the conflict set for calculating a concept exceeds schedule time,
Then stop by force, retains the conflict found.
Step 3 constructs objective function according to practical application, and is constructed and constrained according to each conflict；Wherein, it is looked for all
To conflict merge in a set CONF, for the conflict set progress model construction:
Step 3-1, all different axioms in conflict set are obtained, set S is constitutedunion；
It step 3-2, is set SunionIn each axiom construct a binary variable, obtain binary variable set X, in this way
Variable can only value 0 or 1；
Step 3-3, construct optimization object function Z: when thinking that each axiom is of equal importance, objective function is institute in X
There is the sum of variable；When considering weight, objective function is the sum of the weighting of all variables in X；
Step 3-4, for each conflict conf in CONF, a constraint condition, i.e. each axiom pair in conf are constructed
The sum of variable answered is more than or equal to 1, it can thus be concluded that constraint set C.
Step 4 calls existing integral linear programming solver to be solved, and obtain first variable is assigned conduct
Output；Traditional ILP solver (such as CPlex) is called, solves objective function Z most in the case where meeting and constraining set C
The variable obtained when small value assigns Sassi。
Step 5, the solution for assigning building final according to the variable that solver returns, are deleted in the program from ontology
Axiom can solve given logical contradiction；According to SassiFinal solution is constructed, i.e. acquisition SassiIntermediate value is 1
The corresponding axiom of variable, the set of these axioms are exactly the scheme for solving given conflict CONF.
As an implementation, this implementation provides the main process for solving logical contradiction, proposes to solve logical contradiction
ILP model will calculate the problem of needing the axiom deleted and be converted into finding the problem of carrying out best allotting to given variable, and gives
Two algorithms realize the model out, finally provide Experimental Comparison result.
Specifically:
1. solving the main process of logical contradiction
Fig. 1 gives the main process for solving logical contradiction.Although method proposed by the present invention both can handle logic not
Unanimously, it is uncoordinated also to can handle logic, but only considers that logic is uncoordinated in this implementation.During Fig. 1 is provided, first
It is the selection or building of ontology, can be selected from existing ontology library, or the existing ontology construction tool of utilization (such as
Prot é g é, https: //protege.stanford.edu/) it is constructed.In view of having the quantity to conflict in uncoordinated ontology
With scale without regularity, in addition to some reality, this is external in the test assessment for this implementations, and going back self-developing and constructing some has rule
The ontology of rule.Conflict herein refers to that minimum can not meet and keeps subset (minimal unsatisfiability-
preserving subset)。
For given uncoordinated ontology, by call existing ontology debugging tool (such as RaDON, https: //
Github.com/qiuji123/ilpConflicts conflict set) is calculated.Since an ontology may can not expire comprising more
Sufficient concept or one can not meet concept and be related to more conflict, therefore preset a time threshold (such as 1000 seconds), for
The select concept that can not each meet calculates conflict set at the appointed time.Then, all conflicts found are merged
In one set CONF, duplicate conflict is removed.
Next, constructing ILP model based on conflict set CONF, i.e. building objective function and constraint recalls traditional ILP
Solver (such as Cplex, https: //www.ibm.com/analytics/cplex-optimizer) obtains first variable
It assigns.According to assigning intermediate value to be that 1 variable finds corresponding axiom, these axioms just constitute the solution party for solving given conflict
Case.That is, can solve to give in the ontology rushes from the axiom removed in such solution in given ontology
It is prominent.
2. solving the ILP model of logical contradiction
Here the formal definitions for solving the ILP model of logical contradiction are provided.Assuming that CONF (O) is a punching of ontology O
Prominent set, i.e. CONF (O)={ conf1, conf2..., confm}.Merge the conflict in CONF first, obtains all different axioms
Set Sunion={ ax1, ax2..., axn, then for each axiom ax in setjConstruct a binary variable xj(j
=1 ..., n), wherein variable can only value 0 or 1.Solve the problems, such as that these conflicts become to find in the feelings for meeting m constraint
The obtained variable of objective function z is minimized under condition to assign:
ci: AixT>=1, i=1 ..., m
Wherein, m is the quantity of conflict, and n is SunionSize.First formula is objective function, i.e., all variables add
Power is summed, wherein xjWith wjRespectively indicate the corresponding binary variable of j-th of axiom and coefficient.Second formula is for each punching
Prominent confiConstruct a constraint ci, A in constraint definitioni=(ai1, ai2..., ain) it is a coefficient vector, x=(x1,
x2..., xn) it is the vector being made of all variables.Under normal circumstances, work as confiInclude axiom axj, corresponding coefficient aij's
Value is set as 1, is otherwise 0.The value of coefficient in first formula depends on specific demand, the specific calculation being provided below
It is determined in method.
According to the description of above-mentioned ILP model it is found that one conflict it is corresponding constraint be exactly in the conflict axiom to dependent variable
The sum of have to be larger than equal to 1, such constraint guarantees that the corresponding variable-value of at least one axiom is 1 in each conflict, i.e.,
Each conflict must have an axiom to be included in final solution.
This model is the universal model of logical contradiction in the various application scenarios of processing.Such as ontology repairing, ontology
The scenes such as mapping repairing and ontology amendment can meet specific needs by the value of coefficient in setting constraint.When repairing is single originally
When body, it is believed that each axiom in conflict may be used to delete, and the coefficient in constraint is disposed as 1.When amendment ontology
When, it is assumed that new information is more more reliable than existing information, is set as belonging to the corresponding coefficient of new axiom in conflict
0, other are 1.In this way, new axiom would not be deleted.When repairing Ontology Mapping, often assume two source ontologies be can
It leans on, and there may be problems by the mapping of tools build.Therefore, for mapping coefficient appended by corresponding axiom in conflict
It is set as 1, other are 0.The present invention is directed to all axioms at present all there is the case where removable property to be introduced, other situations can
Coefficient setting is carried out according to above content.
3. the algorithm of the solution logical contradiction based on ILP
This implementation proposes all axiom algorithms of equal importance based on ILP model of view first, and the algorithm is with one
Ontology O and one group of conflict CONF (O) therein are input, export the solution S for solving given conflict setremove。
In this algorithm, it is necessary first to the union for calculating all conflicts in CONF (O), conflicted in different axioms
Set Sunion, it is then SunionIn each axiom distribute a variable, obtain variables set X.Since each axiom is of equal importance,
Therefore the coefficient in objective function Z is disposed as 1, which just indicates the sum of all variables.When constructing constraint set, for every
A conflict constructs its variable and the constraint more than or equal to 1.Based on objective function Z and constraint set C, an ILP solver meter is called
Calculation, which meets in C, to be minimized objective function and obtains an appointment S in the case where all constraintsassi, i.e., the value of each variable be 1 or
The distribution of person 0.Variate-value is 1, then illustrates that corresponding axiom should be included in final solution, otherwise should not
Occur.Therefore, according to SassiThe variable that intermediate value is 1 obtains corresponding axiom, can find final solution Sremove。
It is clear that since the optimization aim of the algorithm is to minimize given objective function, and this objective function is
The sum of all variables, variable can only value 1 or 0, therefore by solver obtain appointment so that value for 1 variable number most
Few, the axiom for including in final scheme is also just minimum, therefore being resolved scheme is one for solving the base of given conflict
The smallest axiom collection of number.
When handling Ontology Mapping or those have the ontology of weight, it is typically desirable to delete the feelings for lacking axiom as far as possible
Retain weight information as much as possible under condition, proposes second algorithm (as follows) based on ILP for this this implementation.The algorithm is with
The main distinction of one algorithm is the building of objective function, i.e., in this way can be with using the weight of axiom as the coefficient of objective function
So that the axiom finally removed has the characteristics that weight and minimum.Certainly, in order to reach weight and minimum, final solution
It cannot be guaranteed the smallest characteristic of radix.
The two algorithms are suitable for different scenes, and one is used to look for the smallest solution of radix, another is used for
Look for weight and the smallest scheme.Weight is usually to be obtained during constructing ontology by study, or utilize certain plans
Approximation calculates.For example, the frequency occurred in conflict set according to axiom, removing the size that has an impact of axiom or axiom
The weight of the calculating axiom such as source information.
4. test assessment
In order to assess proposition algorithm efficiency and effect (i.e. removal axiom number), this implementations calculates two of proposition
Method (being indicated respectively with Alg1 and Alg2) is compared with based on the algorithm for touching Ji Shu.Here indicate that directly collection is touched in application with Hst
Algorithm in tree algorithm to given conflict set, from it is all find touch concentration return it is one the smallest；It is indicated with Hstscore
HST algorithm is applied to the algorithm in the subset of conflict set, i.e., extracts those of frequency of occurrences highest axiom from each conflict
Form subset；HstWeight is all subsets that HST algorithm is applied to those of the minimum axiom structure of weight in each conflict
On.Experimental evaluation carries out on the notebook of 2.4GHz Intel (R) Core (TM) 2Duo CPU, maximum memory setting
For 4GB.
Fig. 2 to Fig. 4 provides that Alg1, Hst and HstScore are compared as a result, wherein each figure shows that 11 include 10 to 20
The ontology of a different conflict does not have any shared axiom between these conflicts.In addition, the size of each conflict is distinguished in three width figures
It is 3,4 and 5 axioms.It can be become apparent from from these figures, Alg1 has very high efficiency, and shows very steady
Fixed, regardless of number of collisions or conflict size change, Alg1, which is substantially, found a solution party just with about 0.4 second
Case, and other methods are then in most cases needed using 100 seconds or more, or even are completed within the stipulated time (1000 seconds)
It does not calculate.Hst and HstScore has similar efficiency, this is because the conflict in the ontology of test is irrelevant, causes
The two algorithms are all HST algorithm to be applied on same conflict set, therefore have same search space.
Table 1 carries out real ontology the test result of contradiction solution
Table 1 gives the test result that contradiction solution is carried out for real ontology, and wherein UC expression can not meet concept
Quantity, CONF indicate the number of collisions found at the appointed time.Here ontology be it is select from Network ontology library,
Concept and more conflict can not be met with more.This test, which is only selected, can not partly or entirely meet concept and surveyed
Examination, such as ontology Or1, can not meet in concept from 62 and choose 6.Since the conflict in these real ontologies all has
Very high plyability, that is to say, that same axiom possibly is present in many conflicts.Such as from ontology Or2In find 412
Conflict, and at least there was only 1 axiom in solution, illustrate in these conflicts all comprising the axiom.In this case, Hst
With HstScore efficiency with higher.In addition, Alg1 and Hst may be used from the point of view of the axiom number for including according to solution every time
To find the smallest solution of radix, and HstScore is then because the selection of subset may remove more axiom.
Table 2 carries out the ontology comprising weight information the test result of contradiction solution
Table 2 give Alg2 and Hst and HstWeight comparison as a result, wherein each ontology is by by two sources
Ontology is mapped with it merge obtained from, conferencing data of the data in famous Ontology Mapping system evaluation platform OAEI
Collection.From efficiency, Alg2 is similar to Alg1, typically takes from the time less than 0.4 second and calculates a solution.Hst
The time spent with HstWeight is also especially few, and the conflict being primarily due in these ontologies all has very high plyability.From solution
Certainly scheme SremoveFrom the point of view of the sum of the quantity (i.e. num) of middle axiom and weight (i.e. sum), Alg2 can guarantee to find every time really
Solution have the characteristics that weight and minimum, only it cannot be guaranteed that delete axiom number it is minimum.For example, for the last one
Ontology, Alg2 removes 3 axioms, and Hst need to only remove 2 axioms.
The present invention is in view of the efficient of ILP and with the similar of logical contradiction processing problem, and definition is for solving logic lance first
Then the ILP model of shield proposes that the specific algorithm for realizing the model, one of algorithm do not consider weight, be used for calculating basis
The smallest axiom collection；Another algorithm considers weight, for calculating weight and the smallest axiom collection.By Experimental comparison, it is based on
The algorithm of ILP often only needs one scheme of acquisition in 0.4 second, and other algorithms need to spend 100 seconds or more in many cases.
It although an embodiment of the present invention has been shown and described, for the ordinary skill in the art, can be with
A variety of variations, modification, replacement can be carried out to these embodiments without departing from the principles and spirit of the present invention by understanding
And modification, the scope of the present invention is defined by the appended.
Claims (8)
1. the ontology logical contradiction processing method based on integral linear programming, which comprises the following steps:
Step 1, the source for providing ontology；
Step 2 calculates conflict by ontology debugging tool, and to each conflict calculating and setting time threshold that can not meet concept
Value；
Step 3 constructs objective function according to practical application, and is constructed and constrained according to each conflict；
Step 4 calls existing integral linear programming solver to be solved, and obtain first variable is assigned as defeated
Out；
Step 5, the solution for assigning building final according to the variable that solver returns, from the public affairs deleted in ontology in the program
Reason can solve given logical contradiction.
2. the ontology logical contradiction processing method according to claim 1 based on integral linear programming, which is characterized in that step
Rapid 1 further comprises: selecting from existing ontology library or constructs a uncoordinated ontology O by ontology construction tool, then therefrom
Concept can not completely or partially be met by selecting.
3. the ontology logical contradiction processing method according to claim 1 based on integral linear programming, which is characterized in that step
Rapid 2 further comprise: minimal conflict sets are calculated using ontology debugging tool, if the conflict set for calculating a concept is more than
Stipulated time then stops by force, retains the conflict found.
4. the ontology logical contradiction processing method according to claim 1 based on integral linear programming, which is characterized in that step
Rapid 3 further comprise: all conflicts found being merged in a set CONF, carry out model construction for the conflict set.
5. the ontology logical contradiction processing method according to claim 4 based on integral linear programming, which is characterized in that right
The step of conflict set in step 3 carries out model construction further comprises:
Step 3-1, all different axioms in conflict set are obtained, set S is constitutedunion；
It step 3-2, is set SunionIn each axiom construct a binary variable, obtain binary variable set X, such change
Amount can only value 0 or 1；
Step 3-3, construct optimization object function Z: when thinking that each axiom is of equal importance, objective function is all changes in X
The sum of amount；When considering weight, objective function is the sum of the weighting of all variables in X；
Step 3-4, for each conflict conf in CONF, a constraint condition is constructed, i.e. each axiom is corresponding in conf
The sum of variable is more than or equal to 1, it can thus be concluded that constraint set C.
6. the ontology logical contradiction processing method according to claim 5 based on integral linear programming, which is characterized in that step
Rapid 4 further comprise: calling existing ILP solver, the minimum of objective function Z is solved in the case where meeting and constraining set C
The variable obtained when value assigns Sassi。
7. the ontology logical contradiction processing method according to claim 6 based on integral linear programming, which is characterized in that step
The ILP solver called in rapid 4 includes CPlex.
8. the ontology logical contradiction processing method according to claim 6 or 7 based on integral linear programming, feature exist
In step 5 further comprises: according to SassiFinal solution is constructed, i.e. acquisition SassiThe corresponding public affairs of variable that intermediate value is 1
Reason, the set of these axioms are exactly the scheme for solving given conflict CONF.
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