Answering queries that may have results in the future: a case study in food science Rallou Thomopoulosa,c,∗, Jean-R´emi Bourgueta , Bernard Cuqa , Amadou Ndiayeb a IATE

Joint Research Unit, INRA-Supagro-UM2-CIRAD, Montpellier, France b USBB, CNRS-INRA-Univ. Bordeaux I, Talence, France c LIRMM, CNRS-Univ. Montpellier II, Montpellier, France

Abstract This paper presents a method to represent the evolution of objects during their life cycle, using a logic- and graph-based knowledge representation model. An extension is proposed in order to answer “prospective queries”, concerning the achievement, in the future, of the searched piece of knowledge. A case study in the field of cereal transformation illustrates the proposed approach. Keywords: knowledge representation, query answering, conceptual graphs

1. Introduction An essential feature that is expected from a knowledge based system is to answer queries, i.e. to be able to determine if a piece of information (the query) can be deduced from the knowledge base. We focus on the two following issues: (i) taking into account the “life cycle” of objects in query answering, by considering queries such as e.g. “can one expect – in the future – a food product that is rich in vitamins ?” (ii) providing an intuitive and easily readable formalism to the end users, who are not computer science specialists. However mostly used knowledge representation formalisms are expressed in first-order logic formulas and difficult to handle for non-specialists. Therefore we are interested ∗ Corresponding

author Email addresses: [email protected] (Rallou Thomopoulos), [email protected] (Jean-R´ emi Bourguet), [email protected] (Bernard Cuq), [email protected] (Amadou Ndiaye)

Preprint submitted to Elsevier

December 16, 2009

in the conceptual graph model, which is currently, in artificial intelligence, the only logic-based model that has an equivalent interpretation in graph theory, i.e. graph representations have interpretations in first-order logic, and graph operations have equivalent logical deductions [1]. The question is thus to introduce, in the conceptual graph model, a way of representing – and reasoning with – information about objects life cycle, that is, to take into account their evolution. This work is the first one to introduce this dimension in the conceptual graph model with respect to the graph/logic equivalence of the model. Existing studies have already shown the interest of this model compared to other available formalisms, in particular in terms of interpretability [2, 3], but also concerning soundness and completeness. We thus rely on these works for the comparison with other methods. Section 2 presents related work and briefly exposes the conceptual graph model. Section 3 gives our contributions concerning the “evolves into” relation and prospective queries. A case study concerning food quality prediction is presented in Section 4. Section 5 proposes some future directions. 2. Background Related Work. Several studies have dealt with the representation of time, in particular Prior’s fundamental work in first-order and hybrid logic [4]. Prior proposes four grades of representation, the first two grades being in first-order logic. The first grade defines tenses entirely in terms of objective instants and an earlier-later relation. The second grade distinguishes a particular instant, the ‘Now’, as a primitive notion treated as a constant. A proposition p with no explicit temporal reference is not considered as incomplete, but interpreted as T (N ow, p) (“p is true now”). F p, “it will be the case that p”, is defined as a short-hand for T (N ow, F p), “there exists some instant t which is later than now, and p is true at t” (and similarly for the past tense, P p). This second grade is of particular interest here, since it corresponds to the assumption made in a classic knowledge representation model without time dimension (as in the classic conceptual graph model), where a proposition is interpreted as present. 2

In the conceptual graph model, previous work has considered the introduction of temporal features. [5] extends the conceptual graphs with “demons” that take concepts as inputs, and assert or retract concepts as an output. [6] extends these proposals by allowing conceptual graphs as inputs and ouputs, which is applied in [7]. However our concern here is different since it consists in extending query answering.In ontology research, some studies have dealt with causal and time concept modeling, such as [8]. However the question considered in [8] concerns the temporal granularity of temporal relations, i.e. how long the time intervals in causal relations. These are modeled by time concepts called causal time scales. In this paper, we do not consider time granularity, nor a deep modeling of a time axis, since we describe evolution of an object in terms of simple anteriority/posteriority relations, for query-answering purposes. The Classic Conceptual Graph Model. The Conceptual Graph (or CG) model [9] is a knowledge representation formalism based on labelled graphs. We use the formalization presented in [1]. The support provides the ground vocabulary (the “ontology”) used to build the knowledge base: types of concepts, instances, and types of relations linking the concepts. The set of concept types (resp. of relation types) is partially ordered by the “kind of” relation. The conceptual graphs, built upon the support, are composed of two kinds of vertices, concept vertices (in rectangles) linked by relation vertices (in ovals). The set of CGs is partially pre-ordered by the specialization relation (denoted ≤), which can be computed by the projection operation (a graph morphism allow-

ing a restriction of the vertex labels). The projection is a ground operation in the CG model since it allows the search for answers, which can be viewed as specializations of a query. The support, the conceptual graphs, and the specialization relation, have a logical interpretation in first-order logic. For instance, the logical interpretation of the conceptual graph represented in Figure 1, is the following: ∃x, y, z, w (Durum wheat(x) ∧ P rocessing(y) ∧ P rotein(z) ∧ High content(w) ∧ undergoes(x, y) ∧ contains(x, z) ∧ characterized(z, w)).

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Figure 1: Example of conceptual graph

3. Main Focus In this section, we consider the hypothesis that an object may become, during its life cycle, a different object but conserves its properties, which is a first approximation. We propose a query answering method adapted to this assumption, which makes sense in the application case, as a qualitative approach: the properties of the end food products (for instance, nutritional properties such as vitamin content, glycemic index, etc.) depend on the raw material used and on processing conditions. It is thus sensible to consider that, for a given property, a high-quality raw material is more likely to provide a high-quality end product. 3.1. Enrichment of the support with the “evolves into” relation In addition to the “kind of” relation, we introduce the “evolves into” ree

lation (denoted →) ordering the concept type set of the support. Its logical interpretation is based on Prior’s second grade.

Logical Interpretation. For two concept types C and C’ linked by the “evolves e

into” relation, the associated logical semantics we propose, φ(C→C’), can be formulated as follows (I is the set of individual marker): e

φ(C→C’) that is:

∀ x ∈ I, C(x) → FC’(x)

∀ x ∈ I, T(t, C(x)) → ∃ t1 : t≤ t1 ∧ T(t1 , C’(x)).

E.g. let “Durum wheat” and “Semolina” be two concept types linked by the “evolves into” relation. The associated logical interpretation is the formula: e

φ(Durum wheat→Semolina)

that is:

∀ x ∈ I, Durum wheat(x) → FSemolina(x)

∀ x ∈ I, T(t, Durum wheat(x)) → ∃ t1 : t≤ t1 ∧ T(t1 , Semolina(x)).

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e

Properties. Reflexivity: Given a concept type C, φ(C→C) is the following: e

φ(C→C) that is:

∀ x ∈ I, C(x) → FC(x)

∀ x ∈ I, T(t, C(x)) → ∃ t1 : t ≤ t1 ∧ T(t1 ,C(x))

The reflexivity property is obtained for t = t1 . Transitivity: Given three concept types C, C’ and C �� such that C evolves into C’ and C’ evolves into C”, we have: e

φ(C→C’) that is: e

φ(C’→C”) that is:

∀ x ∈ I, C(x) → FC’(x)

∀ x ∈ I, T(t, C(x)) → ∃ t1 : t≤ t1 ∧ T(t1 , C’(x))

and

∀ x ∈ I, C’(x) → FC”(x)

∀ x ∈ I, T(t1 , C’(x)) → ∃ t2 : t1 ≤ t2 ∧ T(t2 , C”(x))

Hence by transitivity of the “≤” relation we obtain: ∀ x ∈ I, T(t, C(x)) → ∃ t2 : t≤ t2 ∧ T(t2 , C”(x)) that is:

∀ x ∈ I, C(x) → FC”(x)

i.e.

e

φ(C→C”)

The transitivity property is thus obtained.The “evolves into” relation being reflexive and transitive, it is a partial preorder on the set of concept types. 3.2. Prospective queries Scope. A query in the CG model is expressed in the same formalism as a fact, by a conceptual graph. For example, Figure 2 represents the query: “is there a semolina containing a high content in protein ?”. It is a classical query, whose answer consists in deciding whether this information can be deduced from the knowledge base. It is evaluated using the projection operation. We are now

Figure 2: Example of query

interested in queries about the possible future occurrence of a given piece of knowledge: can this information be obtained from the knowledge base extended to the “evolves into” relation? We call such queries prospective queries. E.g. the conceptual graph of Figure 2 is then interpreted as the prospective query: “can one expect to obtain a semolina containing a high content in protein?”. 5

Answer to a prospective query. An answer to a prospective query is based on an extension of the projection operation, that takes into account the “evolves into” relation. Thus the projection operation has to be extended in order to evaluate if a conceptual graph of the knowledge base is an answer to a prospective query. The extended projection operation we propose remains a graph morphism that allows a substitution of the vertices labels [1], except that this substitution is now based on the specialization relation OR the “evolves into” relation: a concept type may be substituted by a more specialized one (with the meaning of the “kind of” relation) OR by a predecessor through the “evolves into” relation. E.g. using this extended projection operation, the conceptual graph of Figure 1 is an answer to the query of Figure 2, interpreted as a prospective query. Complexity. The problem of the existence of a projection from a conceptual graph into another is NP-complete, however polynomial cases exist, such as the problem of the existence of a projection from an acyclic graph into a graph, for which a polynomial algorithm has been proposed [1]. We restrict the queries we use to acyclic graphs so as to remain in this case. The problem remains polynomial in the case of prospective queries, with the hypothesis that comparisons between two concept types to test if they are linked by the “evolves into” relation can be done in constant time. 4. Case Study in food quality prediction 4.1. Context and description of the case study A knowledge management system concerning the processing and qualities of cereal food products has been designed. It gathers two kinds of information: “technical” information defined by the 29 unit operations which are involved in transformation from raw materials to end products (e.g. grinding, storage, drying, etc), and “quality” information defined by 56 criteria used to represent the end-qualities of food products, according to three aspects: organoleptic, nutritional and safety properties (e.g. colors, vitamins, pesticides, etc.). For each unit operation composing the transformation process, and for each

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family of product properties, information has been expressed as rules, represented in the conceptual graph model using the CoGUI interface1 . These rules describe the impact of unit operations on product quality. In the following, we more specifically study the case of the impact of drying on the color and texture of pasta products. We will focus on the following rules expressed by domain experts. The representation of Rule 2 in the conceptual graph model is shown as an example in Figure 3a. Pasta color

(Rule 1) high temperature drying, if applied at the beginning of cycle, inactivates peroxydase (Rule 2) peroxydase is responsible for the brown color of pasta (Rule 3) the brown color hides the yellow color of pasta

Texture

(Rule 4) high temperature drying causes protein insolubilisation (Rule 5) protein insolubilisation is responsible for pasta firmness (Rule 6) a high protein content increases protein insolubilisation level.

Moreover we consider the following “evolves into” relations: e

(E1) Durum wheat grain → Semolina

e

and (E2) Semolina → Pasta product.

4.2. Application of the approach to the case study The elicited knowledge is exploited for two uses: •

Use for prediction. Starting from given process conditions, described by a

conceptual graph, all the rules whose hypotheses are more general can be applied in “forward” chaining, producing a final conceptual graph that represents the expected result. Moreover, the “evolves into” relations provide supplementary knowledge about object evolution, which can be combined with rule knowledge to provide a prediction. The conceptual graph of Figure 3b represents the following information: “the durum wheat grain Bidi17 contains active peroxydase”. e

It can be combined with the “evolves into” relation Durum wheat grain → Pasta

product, obtained from (E1) and (E2) by transitivity, to produce the prediction of Figure 3c. The rule 2, represented in Figure 3a, can be applied to the conceptual graph of Figure 3c, since the latter is a specialization of rule 2 hypothesis. 1 http://www.lirmm.fr/cogui/

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Therefore we can infer the conclusion of the rule, which leads to the conceptual graph of Figure 3d, indicating that the output manufactured product obtained by drying the pasta product Bidi17 is expected to have a brown color.

Figure 3: Example of use of conceptual graph knowledge for prediction

•

Use for reverse engineering. Starting from wanted end-product proper-

ties, described by a conceptual graph query, all the rules whose conclusions are compatible with this graph can be applied in “backward” chaining, suggesting possible process conditions to reach the expected properties. Moreover, using the “evolves into” relations, the queries describing wanted end-product properties can be prospective, allowing for supplementary knowledge about object evolution. For instance, if the objective for the end-product is to produce a firm texture, which is represented by the prospective query of Figure 4a, applying the rule 5 (Figure 4b) in backward chaining allows concluding that protein insolubilisation must be obtained. Then the application of the rule 4 (Figure 4c) in backward chaining indicates that high temperature drying must be applied. Moreover the application of the rule 6 (Figure 4d) in backward chaining indicates that a high protein content in pasta product must be selected. Using the e

“evolves into” relation Durum wheat grain → Pasta product allows inferring that the conceptual graph represented in Figure 4e is an answer to the prospective 8

query, i.e. the MACS-1967 durum wheat variety should be a good candidate to obtain a firm texture in the resulting pasta product.

Figure 4: Example of use of conceptual graph knowledge for reverse engineering

5. Conclusion and Future Trends In this paper we presented a method to represent the evolution of objects during their life cycle, using a logic- and graph-based knowledge representation model, namely the conceptual graph model, by introducing the “evolves into” relation. We gave its logical interpretation and proposed an extension of the projection operation to answer “prospective queries”, that is, queries concerning the achievement, in the future, of the piece of knowledge that is searched.

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The proposed approach is applied to a case study in food quality prediction. This case study, undertaken in tight collaboration with domain experts, demonstrated the added value of taking into account knowledge about object evolution, by providing a gain in relevance of the prediction and reverse engineering results obtained by the method. The same approach can be adopted in other (including non-food) domains, e.g. concerning manufacturing which processes raw material into transformed products. It is currently considered for application in the hevea chain, which produces natural rubber with expected end properties. In this approach, we made a strong hypothesis: the conservation of properties in time. Future work will focus on the management of properties that are likely to change, which is more complex since it implies to take into account the uncertainty of objects evolution in time. Another future objective consists in providing answers indicating, not only whether a piece of knowledge will occur, but also how it will be obtained. [1] M. Chein, M.-L. Mugnier, Graph-based Knowledge Representation – Computational Foundations of Conceptual Graphs, Advanced Information and Knowledge Processing, Springer, London, 2009. [2] C. Bos, B. Botella, P. Vanheeghe, Modeling and Simulating Human Behaviors with Conceptual Graphs, in: Proc. of ICCS’97, Vol. 1257 of LNAI, Springer, 1997, pp. 275–289. [3] D. Genest, Extension of the conceptual graph model for information retrieval, Ph.D. thesis, University Montpellier II (Dec. 2000). [4] A. Prior, Tense Logic and the Logic of Earlier and Later. In A.N Prior, Papers on Time and Tense, Oxford University press, 1968. [5] H. S. Delugach, Dynamic assertion and retractation of conceptual graphs, in: Proc. 6th Annual Workshop on Conceptual Graphs, SUNY Binghamton, 1991, pp. 15–28. [6] G. W. Mineau, From actors to processes: The representation of dynamic knowledge using conceptual graphs, in: Proc. ICCS’98, Vol. 1453 of LNAI, Springer-Verlag Berlin Heidelberg, 1998, pp. 65–79. [7] D. Benn, D. Corbett, An application of the process mechanism to a room allocation problem using the pcg language, in: Proc. ICCS’01, Vol. 2120 of LNAI, SpringerVerlag Berlin Heidelberg, 2001, pp. 360–376. [8] Y. Kitamura, M. Ikeda, R. Mizoguchi, A causal time ontology for qualitative reasoning, in: IJCAI (1), 1997, pp. 501–507. [9] J. F. Sowa, Conceptual Structures: Information Processing in Mind and Machine, Addison-Wesley, 1984.

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