This research work is devoted to the development of a knowledge base for solving the current problem of forecasting the phase stability of solid solutions. Knowledge bases mean a set of facts and inference rules that allow logical conclusion and purposeful processing of information. The most important property of information stored in knowledge bases is the reliability of specific and generalized information in the database and the relevance of the original information obtained using the rules of inference embedded in the knowledge base. The best knowledge bases include the most relevant, reliable and fresh information, have perfect information search systems, a carefully thought-out structure and format of knowledge. The expert system embodies the methodology of adapting the algorithm of successful solutions from one sphere of scientific and practical activity to another. With the spread of computer technologies, it is an identical intelligent computer program that contains the knowledge and analytical abilities of one or more experts in some field of application and is able to draw logical conclusions based on this knowledge, thereby providing a solution to specific tasks. An intelligent information system (IIS) is one of the types of automated information systems, which is a complex of software, linguistic and logical-mathematical tools for the implementation of the main task, which usually consists of data interpretation and forecasting. Data interpretation is one of the traditional tasks for expert systems. Interpretation means the process of determining the content of data, the results of which must be agreed and correct. A multivariate analysis of the data is usually assumed, and the findings from this model form the basis for probabilistic estimates. Forecasting allows you to predict the consequences of some events or phenomena based on the analysis of available data. A parametric dynamic model is usually used in the forecasting system, in which parameter values are set for a given situation. As a result of the development, a knowledge base model was built for predicting the phase stability of solid solutions using a set of production rules, predicates, functions and operators.
Production rules are a form of representation of human knowledge in the form of sentences of the IF (condition), THEN (action) type. Rules provide a formal way to present recommendations, guidelines, or strategies. They are ideal in cases where knowledge of the subject area arises from empirical associations accumulated over years of work on solving problems in a particular field.
A production model is a set of production rules, which, on the one hand, is close to logical models, which allows you to organize effective derivation procedures on it, and on the other hand, reflects knowledge more clearly.
Production rules are used in artificial intelligence systems (for example, expert systems) [
An expert system is a methodology for adapting the algorithm of successful solutions from one
sphere of scientific and practical activity to another. With the spread of computer technologies, it is an
identical (similar, based on an optimizing algorithm or heuristics) intelligent computer program that
contains the knowledge and analytical abilities of one or more experts in some field of application and
is able to make logical conclusions based on this knowledge , thereby ensuring the solution of specific
tasks (consulting, training, diagnosis, testing, design, etc.) without the participation of an expert (a
specialist in a specific problem area). It is also defined as a system that uses a knowledge base to solve
tasks (issuing recommendations) in a certain subject area. This class of software was originally
developed by artificial intelligence researchers in the 1960s and 1970s and gained commercial use
beginning in the 1980s. Often, the term knowledge-based system is used as a synonym for an expert
system, however, the capabilities of expert systems are wider than the capabilities of systems based on
deterministic (limited, currently implemented) knowledge [
An intelligent information system (IIS) is one type of automated information system, sometimes IIS
is called a knowledge-based system. IIS is a complex of software, linguistic, and logical-mathematical
tools for the implementation of the main task: supporting human activity and searching for information
in the mode of extended dialogue in natural language [
A production model is a set of production rules, which, on the one hand, is close to logical models, which allows you to organize effective derivation procedures on it, and on the other hand, reflects knowledge more clearly.
Production rules are used in artificial intelligence systems (for example, expert systems) [
An expert system is a methodology for adapting the algorithm of successful solutions from one
sphere of scientific and practical activity to another. With the spread of computer technologies, it is an
identical (similar, based on an optimizing algorithm or heuristics) intelligent computer program that
contains the knowledge and analytical abilities of one or more experts in some field of application and
is able to make logical conclusions based on this knowledge , thereby ensuring the solution of specific
tasks (consulting, training, diagnosis, testing, design, etc.) without the participation of an expert (a
specialist in a specific problem area). It is also defined as a system that uses a knowledge base to solve
tasks (issuing recommendations) in a certain subject area. This class of software was originally
developed by artificial intelligence researchers in the 1960s and 1970s and gained commercial use
beginning in the 1980s. Often, the term knowledge-based system is used as a synonym for an expert
system, however, the capabilities of expert systems are wider than the capabilities of systems based on
deterministic (limited, currently implemented) knowledge [
An intelligent information system (IIS) is one type of automated information system, sometimes IIS
is called a knowledge-based system. IIS is a complex of software, linguistic, and logical-mathematical
tools for the implementation of the main task: supporting human activity and searching for information
in the mode of extended dialogue in natural language [
The aim of the article is to develop a knowledge base for an intelligent information system for forecasting the phase stability of solid solutions.
Let's consider the model of the production-type knowledge base for predicting the phase stability of
solid solutions, which consists of a set of relations, production rules, predicates, functions, and operators
[
KnowledgeBase = <Re, Rule, Pr, Func, Op>, (1) consisting of RE relations, production rules, predicates, functions, operators
Rule = {ParamsR, ParamsChargeR, ParamsChargeCoordinationR, TypeAddR, TypeAdd}, (2)
Pr = {A(pi), B(pcj), C(pccn), TypeAddj, Typej, PA(aj), AD(sd), AL(prmj)}, (3) Func= {ElementParams, ElementParamsCharge, ElementParamsCoordination, (4) ElementTypeAdd, ElementType, PredAnalysis, AnalysisData, PredTypeAlgorithm},
Op = {Oprint, Oanalysis, OdataCheck, Opred, OsaveResult, OreturnResult}. (5)
The following are the formal relationships that allow us to consider the informational component of
the "Intelligent system of phase stability of solid solutions" in terms of the relational data model
[
RE = {element_grp, sub_element_grp, element, elm2elm, charge_element, cordination_element, atom_length, sum_atom_length, volume_cell, structure_solid, (6) term_system, tsys_crde, stored_system, stored_result}, where element_grp is a relation for the characteristics of a group of elements; the attributes that make up this relation are: elmg_id (unique ID code of a certain group of elements), elmg_name (name of the group of elements).
element_grp ⊂ elmg_id ✕ elmg_name; (7) sub_element_grp – relation for characteristics of a subgroup of elements; the attributes that make up this relationship denote: selmg_id (unique ID code of a certain subgroup of elements), elmg_name (name of the subgroup of elements).
sub_element_grp ⊂ selmg_id ✕ selmg_name; (8) element – relation to characterize a subgroup of elements; the attributes that make up this relationship are: elm_id (unique ID code of a certain element), elm_selmg (subgroup identifier), elm_name (element name), elm_code (chemical code), elm_count (number of element atoms).
element ⊂ elm_id ✕ elm_selmg ✕ elm_name ✕ elm_code ✕ elm_count; (9) elm2elm – relation for the characteristic of a complex element; the attributes that make up this relationship are: e2e_id (unique ID code of a certain complex element), e2e_che_par (parent charge identifier), e2e_che_ch (child charge identifier), e2e_sort (sorting).
elm2elm ⊂ e2e_id ✕ e2e_che_par ✕ e2e_che_ch ✕ e2e_sort; (10) charge_element – relation for characterizing element charges; the attributes that make up this relationship denote: che_id (unique ID code of a certain element charge), che_elm (element identifier), che_value (charge value).
charge_element ⊂ che_id ✕ che_elm ✕ che_value; (11) cordination_element – relation for characterizing charge coordination numbers; the attributes that make up this relationship are: crde_id (unique ID code of a specific charge coordination number), crde_che (element charge identifier), crde_value (coordination number value).
cordination_element ⊂ crde_id ✕ crde_che ✕ crde_value; (12) atom_length – relation for characterizing the atomic lengths between element charges; the attributes that make up this relationship are: atml_id (unique ID code of a certain atomic length between element charges), atml_che_from (identifier of charge of element 1), atml_che_to (identifier of charge of element 2), atml_value (value of atomic lengths), atml_strs (solid solution structure identifier).
atom_length ⊂ atml_id ✕ atml_che_from ✕ atml_che_to✕ atml_value✕ atml_strs; (13) sum_atom_length – relation for characterizing the sum of atomic lengths between element charges; the attributes that make up this relation are: satml_id (unique ID code of a certain sum of atomic lengths between element charges), satml_che_from (identifier of charge of element 1), satml_che_to (identifier of charge of element 2), satml_value (value of sums of atomic lengths), satml_strs (solid solution structure identifier).
sum_atom_length ⊂ satml_id ✕ satml_che_from ✕ satml_che_to✕ satml_value✕ (14) ✕satml_strs; volume_cell – relation for characterizing the volume of cells between element charges; the attributes that make up this relation are: volc_id (unique ID code of a certain volume of cells between element charges), volc_che_from (element charge identifier 1), volc_che_to (element charge identifier 2), volc_value (volume value), volc_strs (identifier solid solution structures).
volume_cell ⊂ volc_id ✕ volc_che_from ✕ volc_che_to✕ volc_value✕ volc_strs; (15) structure_solid – ratio for characterizing the structure of a solid solution; the attributes that make up this relation are: strs_id (unique ID code of a certain solution structure), strs_name (name of a group of elements).
structure_solid ⊂ strs_id ✕ strs_name; (16) term_system – relation for the characteristics of the thermodynamic system; the attributes that make up this relation are: tsys_id (unique ID code of a certain thermodynamic system), tsys_crde (identifier of the coordination element), tsys_elm (identifier of the element).
term_system ⊂ tsys_id ✕ tsys_crde ✕ tsys_elm; (17) tsys_crde – relation for characterizing elements related to a certain thermodynamic system; the attributes that make up this relation are: tsysc_id (unique ID code of a certain element of the thermodynamic system), tsysc_tsys (identifier of the thermodynamic system), tsysc_crde (identifier of the coordination element).
Tsys_crde ⊂ tsysc_id ✕ tsysc_tsys✕ tsysc_crde; (18) stored_system – relation for the characteristics of the given system, which was calculated; the attributes that make up this relation are: stds_id (the unique ID code of certain data about the system that was calculated), stds_strs (the structure identifier of the system), stds_ln1 (the identifier of lanthanide 1), stds_ln2 (the identifier of lanthanide 2), stds_anion (the identifier anion), stds_eps (calculation step).
stored_system ⊂ stds_id ✕ stds_strs ✕ stds_ln1 ✕ stds_ln2 ✕ stds_anion ✕ stds_eps; (19) stored_result – relation to characterize data on system calculations; the attributes that make up this relation are: stdr_id (unique ID code of certain data about the calculated system), stdr_stds (identifier of the calculated system), stdr_x (result x), stdr_x1 (result x1), stdr_x2 (result x2), stdr_t (t result), stdr_t_crit (t_crit result), stdr_q (q result), stdr_method (method result), stdr_err_message (error text). stored_result ⊂ stdr_id ✕ stdr_stds ✕ stdr_x ✕ stdr_x1 ✕ stdr_x2 ✕ stdr_t ✕ (20) ✕ stdr_t_crit ✕ stdr_q ✕ stdr_method ✕ stdr_err_message.
The scheme of formal relations is in the Figure 1 [
By the term element, we will understand the component, which is determined by certain parameters. In general, the parameters change depending on the type of element [11]. Using the id of the element from the element table, it is possible to connect several elements, which later form a complex element. For this, a knowledge base of the production type of the intelligent module "Elements" was developed, which consists of a set of production rules, predicates, functions and operators [1215].
In the process of creating an element, the possibility of adding general parameters to the element is taken into account (ElementParams function). So, for each element, it is necessary to ensure that indicators are obtained from the database. Therefore, if the parameter pi of some i-th element from N is not present in the system, the universal value pdef is chosen, otherwise it is necessary to enter the value pi. Let's formally define ParamsR products:
If A(pi) then ElementParams(pi) else ElementParams (pdef), (21) where the predicate A(pi) is defined as follows:
pi | i {1,2,..., N} A( pi ) True .
Figure 2 shows an example of entering general parameters.
In the process of creating an element, the possibility of adding charge parameters to the element is taken into account (ElementParamsCharge function). So, for each element, it is necessary to ensure the receipt of pointers from the database. Therefore, if the pcj parameter of some j-th element from M is not present in the system, the universal value of pcdef is chosen, otherwise it is necessary to enter the value of pcj. We will formally define ParamsChargeR products:
If B(pcj) then ElementParamsCharge(pcj) else ElementParamsCharge(pcdef), (23) where the predicate B(pcj) is defined as follows: pc j | j {1,2,..., M } B( pc j ) True . (22) (24)
In the process of creating an element, the possibility of entering parameters of the coordination number to the element is taken into account (ElementParamsChargeCoordination function). Yes, for each element, it is necessary to ensure that indicators are obtained from the database. Therefore, if the parameter pccn of some n-th element from K is not present in the system, the universal value pccdef is chosen, otherwise it is necessary to enter the value ParamsChargeCoordinationR products:
If C(pccn) then ElementParamsChargeCoordination(pccn)
else ElementParamsChargeCoordi-nation (pccdef), where the predicate C(pccn) is defined as follows:
pccn | n {1,2,..., K} C( pccn ) True . define
System users can independently edit the type of element they need. In order to support flexibility, a drop-down list in the element window has been developed: "Complex" and "Simple". Through the “Complex” menu, users can select the j-th tapes rj from the LR element table, which are needed to build a complex element (2+ elements) ElementTypeAdd, and through the “Simple” menu, it is possible to select elements (up to 2 elements) in certain j-th fields from the LF table element by the ElementType function. Let's formally define the TypeAddR and TypeR products:
If TypeAddj then ElementTypeAdd(rj) else ElementTypeAdd(Null), (27) where the TypeAddj predicate is defined as follows:
TypeAdd j | j {1,2,..., LR} TypeAdd j True .
If Typej then ElementType(rj) else ElementType(Null), where the Typej predicate is defined as:
Type j | j {1,2,..., LF} Type j True .
In order to visually easily show how an element was created and which elements were entered into the system, a function was created to print the table of PrintElement elements. Actually, each element is formed from a certain set of fields: elm_id (unique id code of a certain element), elm_selmg (subgroup identifier), elm_name (element name), elm_code (chemical code), elm_count (number of element atoms). Formally, the element print operator
Oprint : (elm_id, elm_selmg, elm_name, elm_code, elm_selmg) → PrintElement. (31) Figure 6 shows an example of printing a table of elements.
By the term forecasting, we will understand the component that begins with the moment of analysis, data processing and ends with the output of data on the user interface. Using data from the tables: element, charge_element, coordination_element, volume_cell, term_system, atom_length, sum_atom_length, stored_system, stored_result, analyzing and processing them, it is possible to obtain data that will be displayed on the user interface in the form of a graph and a table. For this, a knowledge base of the production type of the intelligent module "Forecasting" has been developed, which consists of a set of production rules, predicates, functions and operators.
In the forecasting process, data analysis first takes place (PredAnalysis function). For each system, it is necessary to ensure that the indicators of each element are obtained from the database and analyze whether it is possible to make a forecast. Therefore, if the parameter ai of some i-th element from AN is not present in the system, the universal value adef is chosen, otherwise it is necessary to enter the value ai. Let's formally define Analysis products:
If PA(ai) then PredAnalysis(ai) else PredAnalysis(adef), (32) where the predicate PA(ai) is defined as follows: ai | i {1,2,..., AN} PA(ai ) True . (33)
In order to be able to visually easily show which errors occurred during data analysis, a function was created the output of PredAnalysisErr errors. The function must be given a certain set of fields: elm_id (unique ID of a certain system element), strs_id (identifier of the solution structure), elm_id_ln (id of a certain lanthanide), eps (calculation step). Formally, the error output operator during system analysis
Oanalysis : (elm_id, strs_id, elm_id_ln, eps) → PredAnalysisErr. (34) After data analysis, the prediction algorithm is selected (PredTypeAlgorithm function). The system analyzes and compares the presence of parameters in the element from the database, the following parameters are taken into account: interatomic lengths, sum of interatomic lengths, unit cell volume and ionic radius. Therefore, if the prmj parameter of some j-th element from PARAM is missing in the system, the algorithm using prmion ionic radii is selected, otherwise the prmj algorithm is set. Let's formally define Algorithm products:
If AL(prmj) then PredTypeAlgorithm(prmj) else PredTypeAlgorithm(prmion), (38) where the predicate AL(prmj) is defined as follows:
prm j | j {1,2,..., PARAM } AL ( prmi ) True .
For data processing, after setting the type of forecasting algorithm, the Prediction function was created. A certain set of fields must be passed to the function: elm_id (unique id of a certain element of the system), strs_id (identifier of the structure of the solution), elm_id_ln (id of a certain lanthanide), eps (calculation step), algorithm_tp (algorithm type). Formally, the prediction operator has the form
Opred : (elm_id, strs_id, elm_id_ln, eps, algorithm_tp) → Prediction. (40) After data processing, we save the results in specially developed tables stored_system and stored_result. These tables will later be used in the data analysis phase to check whether calculations have been performed previously with the same input data. So, function SaveResult was created.
A certain set of fields must be passed to the function: stds_strs (system structure identifier), stds_ln1 (lanthanide 1 identifier), stds_ln2 (lanthanide 2 identifier), stds_anion (anion identifier), stds_eps (calculation step), stdr_stds (calculated system identifier), stdr_x (result x), stdr_x1 (result x1), stdr_x2 (result x2), stdr_t (result t), stdr_t_crit (result t_crit), stdr_q (result q), stdr_method (result method), stdr_err_message (error text). Formally, the prediction operator has the form:
OsavesRtedsurlt_:x(2stsdtds_rs_ttr,ss,tdstrd_st__lcnr1it,ssttddsr__lnq2,s,tsdtdr_sm_aentihoond, ,sstdtdsr_e_eprsr, _smtdert_hsotdds), →stdSra_vxe,sRtedsru_lxt1., (41) To display the data on the user interface, the ReturnResult function was created. It is necessary to transfer a certain set of fields to the function: stdr_id (unique ID code of data about the calculated system). Formally, the data display operator on the user interface
OreturnResult : (stdr_id) → ReturnResult. (42) Figure 8 shows an example of displaying data on the user interface. (36) (39)
In this work, for the first time, a knowledge base model was created for predicting the phase stability of solid solutions, which, unlike the existing ones, takes into account the unique limit of substitutions of each lanthanide with the help of a set of production rules, predicates, functions and operators, which allows to increase the accuracy calculation of the energy of mixing and to calculate the exact, and not the general, critical decomposition temperature of the corresponding lanthanide.
[11] V. Vysotska, V. Lytvyn, Y. Burov, P. Berezin, M. Emmerich, V. B. Fernandes, Development of Information System for Textual Content Categorizing Based on Ontology, in: CEUR Workshop Proceedings, 2019. URL: https://ceur-ws.org/Vol-2362/paper6.pdf
[12] N. Khairova, S. Petrasova, A. P. S. Gautam, The Logical-Linguistic Model of Fact Extraction from English Texts, in: Proceedings of the International Conference on Information and Software Technologies, 2016, pp. 625–635. doi:10.1007/978-3-319-46254-7_51.
[13] O. Orobinska, J. H. Chauchat, N. Sharonova, Methods and Models of Automatic Ontology Construction for Specialized Domains (case of the Radiation Security), in: Proceedings of the 1st International Conference Computational Linguistics and Intelligent Systems, Kharkiv, Ukraine, 2017, pp. 95–99. URL: https://oldena.lpnu.ua/bitstream/ntb/39462/1/012-095-099.pdf.
[14] O. Bisikalo, Yu. Ivanov, V. Sholota, Modeling the Phenomenological Concepts for Figurative Processing of Natural-Language Constructions, in: Proceedings of the 3rd International Conference on Computational Linguistics and Intelligent Systems, Kharkiv, Ukraine, 2019, pp. 1–11. URL: http://ceur-ws.org/Vol-2362/paper1.pdf.
[15] M. Nokel, N. Loukachevitch, An Experimental Study of Term Extraction for Real InformationRetrieval Thesauri, in: Proceedings of 10th International Conference on Terminology and Artificial Intelligence, Paris, France, 2013, pp. 69–76.