The paper presents an information system dedicated to requirements recommendation and knowledge sharing. It presents methodology of constructing domain knowledge base and application procedure on the example of production technology of Austempered Ductile Iron (ADI). For knowledge representation and reasoning Logic of Plausible Reasoning (LPR) is used. Both equally applicable LPR for formalization the knowledge of foundry technology, as well as the described system solution have the unique character

B. Śnieżyński

D. Wilk-Kołodziejczyk

E. Nawarecki

S. Kluska-Nawarecka

English

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The recommendation system knowledge representation and reasoning procedures under uncertainty for metal casting

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263METALURGIJA 54 (2015) 1, 263-266S. KLUSKA-NAWARECKA, E. NAWARECKI, B. ŚNIEŻYŃSKI, D. WILK-KOŁODZIEJCZYKTHE RECOMMENDATION SYSTEM KNOWLEDGE REPRESENTATION AND REASONING PROCEDURES UNDER UNCERTAINTY FOR METAL CASTINGReceived – Prispjelo: 2014-02-06Accepted – Prihvaćeno: 2014-08-20Review Paper – Pregledni radISSN 0543-5846METABK 54(1) 263-266 (2015)UDC – UDK 669.163:338.984.047/167/168=111S. Kluska-Nawarecka, The Foundry Research Institute, Poland; E. Nawarecki, AGH University of Science and Technology, Poland; B. Śnieżyński, AGH University of Science and Technology, Poland; D. Wilk-Kołodziejczyk, The Foundry Research Institute, Poland, AGH University of Science and Technology, PolandThe paper presents an information system dedicated to requirements recommendation and knowledge sharing. It presents methodology of constructing domain knowledge base and application procedure on the example of pro-duction technology of Austempered Ductile Iron (ADI). For knowledge representation and reasoning Logic of Plau-sible Reasoning (LPR) is used. Both equally applicable LPR for formalization the knowledge of foundry technology, as well as the described system solution have the unique character.Key words: metal casting, the production of Austempered Ductile Iron, recommendation system, Logic of Plausible ReasoningINTRODUCTIONWith highly dynamic changes taking place in the modern industry, which comprise the introduction of new technologies, new raw materials and semi-finished products, the growing demands of customers and the results of research conducted, easy access to current in-formation and domain knowledge becomes the condi-tion of rational planning, rational management of pro-duction facility and effective implementation of the technological process.The specific character of the foundry industry poses specific requirements on the means and tools for knowl-edge acquisition, its formal representation, and later ef-ficient sharing. This specific character is due to the high complexity of the currently applied physico-chemical processes, for which there is no precise mathematical description, and also to the difficulty in measuring the parameters enabling current control of the process [1-6]. As a consequence, both the knowledge sourced from ex-perts, as well as the measurement of technological pa-rameters are of an incomplete and uncertain character.This study presents the concepts of the casting knowledge representation based on the use of the logic of plausible reasoning (LPR), proposed by Collins and Michalski [7-12]. LPR is a relatively new formalism for which there are no extensive data concerning the indus-trial applications, but it seems that it should prove to be very useful precisely in the case of handling the knowl-edge, which is uncertain and incomplete.The presented considerations outline the basic prin-ciples of the operation of an LPR formalism. Against this background, an original solution of the computer-aided information system, designed to collect and share the knowledge in the domain of foundry and metallurgy, has been presented.The implemented solution has a pilot character and is mainly used to verify the desired functionality and therefore at a given stage of work it has been limited to implementation of a relatively simple area of knowl-edge, expressed in the form of LPR formulas. As an ex-ample, the article presents a set of formulas for ductile iron and ADI along with the results of the inference pro-cedures based on the use of these formulas.LOGIC OF PLAUSIBLE REASONING The Logic of Plausible Reasoning (LPR) has been de-veloped as a tool for modeling of human reasoning, and therefore some issues important for applications in the automated reasoning systems (e.g. variables) have not been taken into consideration. On the other hand, in the LPR, some solutions have been introduced that do not seem necessary and make the system implementation and creation of knowledge bases much more difficult. The modified formalism has been designated as LPR0. The language used by LPR0 consists of a countable set of constants C, variables X, the seven relational sym-bols, and logical connectives → and ∧. Formally it is a quadruple: L =(C, X, {V, H, B, E, S, P, N}, {→, ∧}). The relational symbols (V, H, B, E, S, P, N) are used for de-fining relationships:  H–defines the hierarchy between concepts; expres-sion H(o1, o, c) means that o1 is o in a context c; 264  METALURGIJA 54 (2015) 1, 263-266S. KLUSKA-NAWARECKA et al.: THE RECOMMENDATION SYSTEM KNOWLEDGE REPRESENTATION AND REASONING... B–used to present the fact that one object is placed below another one in a hierarchy; V–used for representing statements:  V (o, a, v) is a representation of the fact that object o has an attribute a equal to v;  E–used for representing relationships; the notation E(o1, a1, o2, a2) means that values of attribute a1 of ob-ject o1 depend on attribute a2 of the second object o2;  S–determines similarity between objects; S(o1, o2, c) represents the fact that o1 is similar to o2 in a context c;  P–represents order between concepts: P(o1, o2) means that concept o1 precedes concept o2;  N–used for comparing the concepts; N(o1, o2) means that concept o1 is different from the concept o2.LPR formula means every atomic formula: H(o1, o2, c), B(o1, o2), V(o, a, v), E(o1, a1, o2, a2), S(o1, o2, c), P(o1, o2), N(o1, o2), where o, o1, o2, a, a1, a2, c, vCX, a conjunction of atomic formulas and implications in the form of α1 ∧ α2 ∧ ...αn → V(o, a, v), where nN, n>0. It is assumed that αi has the form of V(oi, ai, vi), P(vi, wi) or N(vi ,wi), and o, oi, a, ai, v, vi, wiCX for 1 ≤ i ≤ n.To take into account the parameters describing the uncertainty and incompleteness of knowledge, the pre-sented formalism should be extended by adding the al-gebra of labels [13, 14]. Label algebra LPR0denotes a pair A =(A, {fri}), where A is a set of labels, while {fri} is a set of functions defined on labels: AAf iirprr |)(|: , where pr(ri) are the premises of rule ri (described be-low). Labelled formula denotes a pair f: p, where f is formula, and p is label. Knowledge base is any finite set of labeled formulas, not containing besides the implica-tion premises any N-type formulas.Inference rules are used to construct the proof of for-mulas – the operation which corresponds to reasoning. Each rule ri has the following form: ppppnn::::2211  (1)Labelled formulas αi: pi are called the premises of ri rule, and formula α: p is called its conclusion. As men-tioned earlier, with labels of the premises, one can cal-culate the labels of conclusion, using label algebra A:   (2)Due to lack of space, only rules that operate on the statement are presented. Index attached to the name of the rule tells us what is transformed: o is an object, and v is the value. These rules are shown in Table 1. GENo and SPECo are generalisation and specialization of ob-jects in statements, SIMo represents reasoning by anal-ogy (similarity) between objects, and MP is classical modus ponens inference rule.Having introduced the inference rules, one can de-fine the proof of the labelled formula φ from a set of labelled formulas KB. The practical use of an LPR for-malism has been made possible by the development of appropriate inference algorithm LPA which searches for the proofs and calculates labels of a given formula using Knowledge Base [15].Table 1  Selected inference Rules operating on the statementsGENo SPECoSIMo MPLPR-BASED INFORMATION SYSTEMSpecialized software allowing to make inferences in LPR0 has been developed. The goal of the system is to provide an inference tool for searching items matching a description given by the user. Architecture of the sys-tem is presented in Figure 1. All the domain knowledge is stored in a Knowledge Base (KB). When user search-es for the information, it provides a query, which is translated into LPR query formula and proof searching algorithm is executed. It returns items matching the query sorted by label values.Query q has the following form:  q = α1 ∧ α2 ∧... ∧ αm (3) where αi has a form of V(oi, ai, vi) or P(vi, vi’). Query q represents description of some concept the user is looking for. It usually contains some variable represent-ing the concept, and the inference algorithm returns substitution for this variable, which represents an an-swer. Software for the inference engine is developed in Java. In Figure 2 one can see the class diagram of the main package. Engine class is responsible for proof searching. Knowledge Base stores all the knowledge available for the inference engine. Proof represents the proof tree being built. It is connected with sub trees by Vertex class. Substitution and Unification Exception classes are used to process variables. To assist knowl-edge base development, graphical user interface has been added (Figure 3).CASTING TECHNOLOGIES KNOWLEDGE BASEIn this section sample Knowledge Base describing casting technologies is presented. It was prepared to 265METALURGIJA 54 (2015) 1, 263-266S. KLUSKA-NAWARECKA et al.: THE RECOMMENDATION SYSTEM KNOWLEDGE REPRESENTATION AND REASONING...demonstrate LPR reasoning method. Figure 4 presents cast material hierarchy. Below selected formulas are presented. Labels rep-resenting uncertainty are omitted for simplicity.V(material, hardness, high) ∧ V(material, strength, high) ∧ V(material, toughness, high) → V (mate-rial, strength, high)V(ductile iron, post-casting treatment, heat treat-ment)V(cast material, strength, high) ∧ V(cast material, abrasibility, low) ∧ (cast material, damping ca-pacity, high) → V(cast material, application, gears)V(cast Hadfield steel, price, high)S(cast Hadfield steel, ADI, parameters)E(ADI, application, ADI, parameters)E(ADI, strength Rm, ADI, austempering tempera-ture)E(ADI, toughness, ADI, austempering time)V(ADI, tempaustenitising, T) P(860, T), ∧ P(T, 950) → V( ADI, hardness, high)H(ADI_1, ADI, all properties)E(ADI, hardness, ADI, all properties)V(ADI, thickness structure, G) ∧ P(G, 13 mm) → V(ADI, price, low)V(ADI_1, thickness Structure, 10mm)E(ADI, hardness, ADI, all properties)V(ADI_1, tempaustenitising, 900)S(ADI, cast high-alloyed steel, strength )E(ADI, resistance to abrasion, ADI, strength)V(cast high-alloyed steel, resistance to abrasion, high)To show the reasoning process, the following prob-lem is considered. Some user wants to get recommenda-tions from the system of what material the rake should be made. He is looking for material M such that its hard-ness is high, the cost is low, and the resistance to abra-sion is high. It is formalized by the following query:V(M, hardness, high)  ∧ V (M, cost, low) ∧ V(M, resist-ance Abrasion, high)Inference algorithm returns the following substitu-tion: M = ADI_1 (4)where ADI_1 is a specific example of ADI (it is a standard product of some company), subjected to spe-cific treatment processes, with certain additions, which are expressed in the knowledge base with appropriate formulas. The following inference process is applied to infer the conclusion (4).Step 1. HardnessThe knowledge base contains the ruleV(ADI, tempaustenitising, T) ∧ P (860, T), P (T, 950)→V(ADI, hardness, high) Using the inference rule SPECo→  for this implica-tion and the following two formulas:H(ADI_1, ADI, all properties) Figure 1 Architecture of LPR-based Information Figure 2 Class diagram of the inference engine packageFigure 3 Knowledge editor windowFigure 4 Hierarchy of cast materials 266  METALURGIJA 54 (2015) 1, 263-266S. KLUSKA-NAWARECKA et al.: THE RECOMMENDATION SYSTEM KNOWLEDGE REPRESENTATION AND REASONING...E(ADI, hardness, ADI, all properties)it is possible to derive specialization of this implica-tion:V(ADI_1, tempaustenitising, T) ∧ P (860, T) ∧ P(T, 950) → V(ADI_1, hardness, high)The knowledge base contains information about ADI_1 austenitising temperature:V(ADI_1, tempaustenitising, 900)hence it can be inferred using MP that V(ADI_1, hardness, high).Step 2. PriceHaving in the knowledge base the formulaV(ADI, thickness Structure, G) ∧ P(G, 13 mm) → V(ADI, price, low)and knowing thatV(ADI_1, thickness Structure, 10mm)the system can infer in a similar way that the cost of production will be correspondingly low:V(ADI_1, price, low).Step 3. Abrasion resistanceA similarity between cast iron and cast high-alloyed steel is used. Knowing that:S(ADI, cast high-alloyed steel, strength)E(ADI, resistance to abrasion, ADI, strength)V(cast high-alloyed steel, resistance to abrasion, high),using the SIMo rule of inference, the following for-mula is derived:V(ADI, resistance to abrasion, high)The above statement is specialised for ADI_1 using SPECo inference rule and the following formulas: H(ADI_1, ADI, all properties)CONCLUSIONSThe paper presents some rules for the representation and sharing of domainknowledge in the area of foundry technologies based on the use of LPR formalism.The presented rules for the description of knowledge in terms of LPR as well as the examples of constructing such knowledge for ductile iron and ADI show that the process of creating the knowledge base is in the case of such notions of much more intuitive character and clos-er to the human way of reasoning than while using con-ventional formalisms - for example, bivalent logic or fuzzy logic.The disclosed reasoning shows how the knowledge gained from the source materials (standards, publica-tions) as well as expert knowledge expressed in natural language can be easily written in the form of rules and theorems of the LPR language.The conducted computational tests confirmed the functionality of the pilot implementation of the system in terms of both inference and generalisation of knowl-edge shared with the help of this system.AcknowledgementsThis paper was made on basis of a research project LIDER/028/593/L-4/12/NCBR/2013REFERENCES[1] R. S. Michalski, A theory and methodology of inductive learning, Artificial Intelligence (1983) 20, 111-161.[2] S. Kluska-Nawarecka, Z. Górny. D. Wilk-Kołodziejczyk, A. Smolarek-Grzyb, The logistic of plausible reasoning in the diagnosis of castings defects, Archives of Metallurgy and Materials, 52 (2007) 3, 375-380.[3] S. Kluska-Nawarecka, et al. The use of LPR (logic of plau-sible reasoning) to obtain information on innovative ca-sting technologies, Archives of Civil and Mechanical En-gineering, 14 (2014) 1, 25-31.[4] J. Pearl, Fusion, propagation, and structuring in bayesian networks, Artificial Intelligence (1986) 29, 241-288.[5] Z. Górny, S. Kluska-Nawarecka, D. Wilk-Kołodziejczyk, Attribute-based knowledge representation in the process of defect diagnosis, Archives Of Metallurgy And Materials 55 (2010) 3, 819-826.[6] S. Kluska-Nawarecka, D. Wilk-Kołodziejczyk, K. Re-gulski, et al. 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Virvou in A Cognitive Theory in an Authoring Tool for Intelligent Tutoring Systems, IEEE International Confe-rence on Systems Man and Cybernetics, Tunisia, 2002, pp. 410-415.[12] M. Virvou and B. Du Boulay, Human plausible reasoning for intelligent help, User Modeling and User-Adapted Inte-raction (1999) 9, 321-375.[13] D. M. Gabbay, LDS –Labelled Deductive Systems, Oxford University Press, 1991, pp. 282-232.[14] B. Śnieżyński, Probabilistic Label Algebra for the Logic of Plausible Reasoning, Intelligent Information Systems 2002, Advances in Soft Computing, M Kłopotek et al. (ed.), vol. 17, Springer, Poland, 2002, pp. 267-277.[15] B. Śnieżyński, Proof Searching Algorithm for the Logic of Plausible Reasoning, Intelligent Information Processing and Web Mining, Advances in Soft Computing, M. Kłopotek et al. (ed.), vol. 22, Springer, Poland, 2003, pp. 393-398.Note:  The responsible translator for English language is Krystyna-Bany-Kowalska, (The Foundry Research Institute, Poland)

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The recommendation system knowledge representation and reasoning procedures under uncertainty for metal casting

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