Abstract. Constructivism is known as either a learning philosophy or a model of knowing. It's possible to say that a successful learning science may be ...
TOWARDS A SEMANTICS-BASED FRAMEWORK FOR MEANING CONSTRUCTION IN CONSTRUCTIVIST INTERACTIONS Farshad Badie Center for Linguistics, Aalborg University (DENMARK)
Abstract Constructivism is known as either a learning philosophy or a model of knowing. It's possible to say that a successful learning science may be constructed and developed based on the proper foundation that is provided by constructivism. Jean Piaget, the originator of constructivism, argued that all learning was mediated by the construction of mental objects that he called schemas. From his point of view, schemas gradually develop into more conceptual mental entities. According to constructivism, a learner and a mentor, can – based on their preconceptions (concept pre-formations), based on their pre-structured knowledge and based on their personal knowings – actively participate in an interaction with each other in order to construct personal knowledge. The most significant objective of constructivism is construction of personal knowledge and its development, and producing the own understanding of a world (universe of discourse) within the interaction. Therefore, the learner and mentor gain an opportunity to attain deeper personal understandings and comprehensions and greater motivations. The main contribution of the present research is the conceptual and logical analysis of meaning construction in constructivist interactions based on my conceptualisation of Definition and Definiteness, Meaning and Meaningfully and Semantic Interpretation. In this research I will analyse meaning construction and meaningful comprehension production within constructivist interactions. I will employ some fundamentals from ‘functions and functionality’ and ‘concept languages or Description Logics (DLs)' in order to analyse the semantics of some concepts and conceptions in the course of work. I will provide a DLs-based formal semantics for analysing meaning construction in constructivism. The main focus will be on my proposed semantic loop that the learner and mentor as intentional participants move through, which organises their personal constructed conceptions in order to construct meanings and produce their meaningful comprehensions. This research will be concerned with meanings and definitions and proposes a new scheme for interpretation based on semantics and on interactions. Keywords: Constructivism, Semantics, Interpretation, Meaning, Description Logics.
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INTRODUCTION AND MOTIVATION
An interaction between two (or more) agents exchanges a number of questions, answers and actions concerning their personal conceptions and conceptualisations. First, I shall emphasise that ‘concept’ is a term that should be used with caution and I need to explain what I mean by this term. The specification of concepts makes a proper background for describing and understanding of conceptions and conceptualisations. Actually there has been a general problem with concepts. For example, in linguistics, in psychology, in philosophy, in metaphysics and in information sciences we may have different notions and visions of what a concept is. So, what I will use and will express under the label of ‘concept' aims at providing a comprehensible characteristics of conceptions and conceptualisations. In my semantic approach, a concept is a linkage between linguistic expressions and the mental images that a human may have in her/his mind, see [6]. For instance, these mental images could be interpreted and seen as the representation of aspects of the world and building the universe of discourse. And, in fact, what is being identified as a conception of an agent within an interaction is her/his act of visualising different concepts and linking her/his expressions with regard to individual mental images and schemas. The context of this research is the interaction between the learner and her/his mentor. Accordingly, I need to focus mainly on multilevel agreement-oriented interactions among learners and mentors. Such interactions could be viewed as a radical constructivist account of the learner’s (and mentor’s) cognition, comprehension and understanding, see [19] for more details. The constructivist account of an agent’s understanding is capable of enabling her/him in developing the individual understandings of the more specified (and complex) concepts with regard to her/his understanding of the general
Proceedings of ICERI2015 Conference 16th-18th November 2015, Seville, Spain
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ISBN: 978-84-608-2657-6
concepts. Producing one's own understanding of a world and developing it during the interactions with the interlocutor could be said to be the most valuable product of the constructivist interactions. Understanding more specified concepts enable learners (and mentors) to develop their own understandings of the underlying systematic processes in reality, and also their understandings of themselves through the universe of discourse. I also need to be careful with the usage of the term Constructivism. Constructivism can be used in many disciplines, see [3]. Generally, it can be classified into two main parts: i.
Constructivism as a learning philosophy and educational theory of learning,
ii.
Constructivism as a model of knowing.
By all means there seems to be a very strong interrelationship between i and ii. The reference [7] has specified constructivism as a theory of knowledge with separated roots in philosophy, psychology and cybernetics. Also, I have observed constructivism as a ‘theory of knowledge and knowing’ in my semantic approach. In my opinion, knowledge is actively constructed based upon the agent’s comprehension of meanings with regard to the definitions of concepts. We will see that the knowledge of a part of the universe of discourse, will be more understandable and comprehensible by both agents after their interactions. The important common background of i and ii is that, when a learner (and even a mentor) participates, based on her/his personal knowings and on her/his pre-structured knowledge, s(he) gains an opportunity to attain a deeper personal comprehension and to develop her/his understanding. And then s(he) will succeed in constructing knowledge. I acknowledge this as the most central assumption of the constructivist interactions. Jean Piaget, the originator of constructivism, argued that all learning was mediated by the construction of mental objects that he called schemas. For Piaget, schemas first emerge as concrete actions and gradually develop into more abstract and conceptual mental entities, see [8], [17], [11], [7], [12]. Considering learning in the framework of constructivism with reference to conversation theory, which is designed by Gordon Pask, the enterprise begins with the negotiation of an agreement between the learner and the mentor to converse about a given domain and learn (and train) about some particular topics and skills in that domain. It could work as an explanatory, heuristic and developmental framework. For more detailed information see [14], [15], [10]. In this research I will focus on the conceptual and the logical analysis of meaning construction in constructivist interactions. As mentioned, knowledge is actively constructed based upon the agent’s comprehension of meanings with regard to the definitions of concepts. So it seems quite important to conceptualise Concept, Meaning and Definition and their interrelationships. I will need to analyse Definition and Definiteness, Meaning and Meaningfully, and Semantic Interpretation within my approach. In order to analyse concepts and conceptions in the process, I will provide a formal semantics relying on Description Logics (DLs), see [1]. DLs is the most well-known knowledge representation formalism. The concepts (and their interrelationships) are used to establish the basic terminology adopted in my modelled pedagogical domain regarding the hierarchical structure. I will analyse meaning construction and meaningful comprehension production within constructivist interactions. My main focus is on my own semantics-based framework ([2]). According to that, learner and mentor as intentional participants move through a semantic loop and organise their personal constructed conceptions in order to construct meanings, to improve the constructed meanings, and to produce their individual meaningful comprehensions. In this research, considering the analysis of definitions and meanings I will develop my framework. What could be offered by learning constructively in this framework in the context of interactions, is ‘a body of thought’ and ‘a semantic model to account for the emergence of the domain of the learner’s (mentor’s) conceptual knowledge’.
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TERMINOLOGY
Description Logics (DLs) is a well-known knowledge representation formalism and represents knowledge in terms of (i) individuals or objects, (ii) concepts or classes, and (iii) roles or relationships. Individuals correspond to constants, concepts to unary predicates, and roles to binary predicates in first order predicate logic (FOL). In DLs individuals are the instances (or members) of a concept. For instance, John as an individual can also be recognised as an instance of the concept Person. Focusing on predicate P, which is one of the most important constructors of the sentences in FOL, we could say that P is capable of covering something, let me name it variable X. Then, we have a P(X). P(X) expresses that P is describing X, see [5]. Reconsidering the predicate P in DLs and naming it a role, we have achieved something that can establish a relationship between various individuals.
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In DLs the concepts could be divided into two types: a. The Atomic Concepts (Concept Names), e.g., Person, Thing, Computer, Logic, Management. An atomic concept is representable by A in DLs. They are very general concepts and could be identified as the labels of the classes of ontologies within ontology representation systems. b. The Complex Concepts (the specified atomic concepts), e.g., FemalePerson, WhiteWing, ComputerScience, InductiveLogicProgramming, ManagementInformationSystems. Obviously, an agent (learner or mentor) could understand an atomic concept easier than its specified case. From another point of view, there are two kinds of atomic symbols. (a) Atomic Concepts, (b) Atomic Roles. From this perspective, atomic symbols are defined as the elementary descriptions from which humans inductively build and construct complex (specified) descriptions by means of concept constructors and role constructors. The set of the main connectors in the base Description Logic is:{ Conjunction (⊓ : and), Disjunction (⊔ : or), Negation (¬ : not), Existential Restriction (∃ : there exists … ), Universal Restriction (∀ : for all ... ), Top Concept (⊤ : everything), Bottom Concept (⊥: nothing) }. A knowledge base in DLs usually consists of the terminological axioms and assertions. Considering C and D as concepts, R and S as roles, and a and b as individuals we have the following terminological axioms: (i) The Concept Inclusion C ⊑ D, (ii) The Role Inclusion R ⊑ S, (iii) The Concept Equality C ≡ D, and (iv) The Role Equality R ≡ S. Additionally, C(a) and R(a,b) denote the concept and the role assertions, see [1], [18]. Example. Anna has been asked to describe the concept Teacher. She conceptualises Teacher by “Teacher is a person who has (at least) one student”. This description has been built up following the inductive rules. Translated into DLs we have: “Teacher ≡ Person ⊓ ∃hasStudent.Person”. This concept description supports the formal, explicit specification of the conceptualisation of the concept Teacher based on Anna’s conception. Obviously, her constructed description for Teacher influences her other conceptions based on Teacher. On the other hand, it’s also obvious that Anna’s description of the concept Teacher is dependent on the concept Student. Therefore, for a stronger and more specified conceptualisation of Teacher, she must describe Student on one higher conceptual level. This conceptual dependency demonstrates that she has been concerned with the taxonomy of various concepts and with the explicit specification of the conceptualisation of the concept Teacher. Actually, she is indirectly getting concerned with an ontology. Suppose that she is an agent in an interaction, and that she will utter her conception of Teacher (and Thus of Student) to her interlocutor. So, she has provided a prescription for building a block of the constructivist learning support system in the context of her interaction.
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EXPLANATION
In this research I assume that an explanation is the actual explaining of definitions and meanings. The main objective of explanations is to shed light on the produced personal comprehension. In this section I will focus on analysis of definitions and meanings. They will be applied in section 5.
3.1
Meaning
Linguistically, meaning is realised as a context-update function, see [9]. So, the input of the meaning function is a context and the output is its updated form. Considering X as a context and X´ as the updated form of X we have: Meaning: X → X´. Any context comprises different types (and different numbers) of concepts, i.e. atomic concepts and specified concepts. Then terminologically we have C ⊑ X. Therefore, I describe a Meaning as a concept-update function like: Meaning : C → C´. I will need to reconsider the meanings while I will be concerned with the interpretation functions in section 4.
3.2
Definition and Definiteness
In a semantics based system a definition can be figured out as a kind of equation whose left-hand side is a concept (the concept that is going to be defined) and whose right-hand side is a description (generally built up using the inductive rules). In the current approach, a definition is a type of introduction. Actually, a description is expressed in order to introduce atomic (and complex) concepts and roles, and their possible combinations for constructing more specified descriptions. In an
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constructivist interaction, the learner and the mentor introduce and define different concepts, which are produced by their individual conceptions and based upon multiple concept descriptions. All these definitions have been constructed over their pre-structured knowledge. Logically, a set of definitions must be ’explicit’ and ’unequivocal’, i.e., not vague and not ambiguous. Example. Though the lenses of Bob’s conception, the concept Spring can be defined as ‘the season of the moderate weather; when all the trees are green’. His description can be translated into a DLsbased formalism. Then, “Spring ≡ Season ⊓ ∃hasModerate.Weather ⊓ ∀hasGreen.Tree”. In fact, he has defined the concept Spring by associating Spring with a description, which has been built up based on his own conception. In a constructivist interaction, any of the agents may define a concept based upon her/his individual conception. Accordingly, regarding the feedbacks of the interlocutor, s(he) modifies and updates her/his definition. I have called it definition updating. Here are two important facts: i.
A defined definition by the learner (mentor) provides a supportive backbone for performing a more developed (and organised) concept description(s).
ii.
A more developed (and more well-organised) concept description supports the learner (mentor) in providing a more understandable meaning on higher levels of interaction.
In this example, the interlocutor can update the Spring’s definition. For instance, s(he) can make the definition more specified and defines Spring by ‘Spring is the season of the moderate weather; when all the trees are green. And April is one of its months’. Equivalently, “Spring ≡ Season ⊓ ∃hasModerate.Weather ⊓ ∀hasGreen.Tree ⊓ ∃hasApril.Month”.
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THE SEMANTIC INTERPRETATION
Generally, to elucidate and to explicate what we mean by something, and to explain our meanings, is noticed as our interpretation of that thing, see [20]. An agent who constructively focuses on the concept description C in an interaction needs to provide a way to determine the truth values of her/his sentences concerning C. Actually, these sentences have all been explained based on her/his mental images of C. Subsequently, s(he) transforms her/his mental images into some linguistic expressions. It’s possible to translate the final linguistic expressions into a description language like DLs. Linguistically, an interpretation is known as the continually adjusted relationship between two salient things: 1. The conventional meanings of the agent's sentences/statements. In other words, the agent’s intention behind her\his expression of those sentences/statements. 2. The actual mental universe of the C, which is based on the accumulated experience of that individual. From the logical point of view, an interpretation is an assignment of meanings to the non-logical symbols and to the non-logical parts of the sentences/statements. The interpretation cannot assign meanings to the logical symbols, e.g., not, and, or, equal, equivalent. An agent is not able to assign any meaning to a description until s(he) interprets all the non logical symbols of that description in her/his mind. Considering C and D as two concepts and R(C,D) as any possible binary relationship between them, an agent could have different interpretations over them. More specifically, the interpretation I assigns to the concept description C and D two sets that contain their interpretation(s). It also assigns to the role R a binary relationship between the elements of those two sets (between the interpretation(s) of C and the interpretation(s) of D), see [16]. In case a given interpretation could assign the value TRUE to a sentence (built up over a concept description) that interpretation is called a model of that sentence. And if an agent’s sentence is assigned the value TRUE for all possible interpretations it would be a tautology model. Designing a proper model can make the definitions adequate. A compassionate mentor and a dutiful learner attempt to provide adequate models for their utterances. They also wish to perform a tautology model in order to satisfy all possible interlocutor’s interpretations and to satisfy the interlocutor’s mentality. From the formal point of view, I observe an interpretation as an assignment of meanings to the nonlogical building blocks of the agent’s language and her/his linguistic expressions. In order to bring forth l the formal semantics of the approach, I employ the function l from a non-empty set Ɗ into the set Ɗ . l Then, l: Ɗ → Ɗ . Ɗ may contain multiple atomic concepts and concept descriptions that the agent has I l in mind. Therefore, the function I assigns to every atomic concept A a set like A (l: A → A ), and to
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l
l
I
every concept C a set like C (l: C → C ), which are both the subsets of the set D . This procedure is definable on every atomic (and described) role. So, considering R as a binary relation between two I l l concepts C and D, there is a R from Ɗ into Ɗ × Ɗ . As mentioned in the analysis of meanings, I need to reconsider the meanings concerning the interpretation functions. Here I figure out a function as a functional role between two concepts. Suppose that C is a concept. The interpretation I interprets Meaning as a functional role if and only if { I (C, C1) , (C, C2) } ⊆ Meaning implies that C1 = C2. Therefore, Meaning (C) = C1 = C2. Supposing that C is a concept, which has been produced based on the agent’s conception. S(he), according to her/his interpretations, produces the Meaning function by meaning C (finding an adequate meaning for it) for her(him)self.
5
MEANING CONSTRUCTION: THE SEMANTIC PROCESS
The primary step towards learning constructively within an interaction can be built up over an asked question or a committed action. The schemata could be seen as different types of concrete actions and questions. The learner (mentor) gradually develops and divides them into more general concepts. A person who undertakes to learn something and to understand it within a constructivist interaction primarily gets concerned with various general concepts related to that thing. More specifically, s(he) 1 gets concerned with forming or reforming concepts.
5.1
Designing Schemata
Obviously, at the beginning the learner has a shallow understanding of what s(he) directs to learn, and of its situation within the universe of discourse, see [13]. The preliminary understanding supports the learner in building various patterns in her/his mind, and any of these patterns describes the learner’s thought over a conception related to a matter. These patterns could be seen as the mental structures. The learner uses these mental structures to organise her/his conceptual knowledge, and to provide strong backbones for her/his interpretations. The learner gradually elaborates the network of her/his 2 general mental structures. Any of these patterns is what has been introduced as a schema that is the most central assumption of the constructivist interactions, see [4]. In my semantic approach schemata are employed to: i.
provide a background for the learner’s concepts,
ii.
specify the learner’s inferences and argumentations,
iii. describe different theories based on terminological axioms and assertions, iv. give sufficient and satisfying conditions for definitions of truth. The most primary phase is Designing Schema, see the Figure 1. I shall emphasise that schemata are the most significant necessities of an adequate model for meaning construction and meaning production in my semantic approach. Note that all mentioned matters relevant for a schema are semantically valid in the case of the mentor as well.
5.2
Concept Construction & Meaning Formulation
From the methodological point of view, the learner is the developer of her/his personal conceptions over the individual designed schemata. S(he) needs to employ inductive rules in order to expand her/his general concepts into more specified ones. Additionally, during the interaction s(he) investigates new concepts and applies them in her/his concept constructions. Hearing any word from the interlocutor, e.g., why, tell, think, compare, mean, map, is conducive to new conceptions and new concepts. As mentioned, a learner may have formed a concept before participating in the interaction. For instance, Mary initially has conceptualised and defined the concept Information System by ‘the Information system is a system whose components are information’. This definition is translatable into “InformationSystem ≡ System ⊓ ∃hasComponent.Information”. Suppose that she utters her definition.
1
http://teachinghistory.org/teaching-materials/teaching-guides/25184
2
See http://plato.stanford.edu/entries/schema and http://www.britannica.com/topic/schema-cognitive
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Later on, regarding the feedbacks produced by the mentor, she will be conduced to performing either a more specified (and accurate) definition or a modified (reformed) definition for the concept Information System. Notice that the collection of formation, transformation and reformation of the concepts is a significant matter in the development of the concept constructions within constructivist interactions. I identify the process “ forming the concept → transforming the concept → reforming the concept “ as the main basis of Concept Construction in my framework, see the Figure 1. The generalisation of various specified concepts supports the learner (and even the mentor) in discovering new concept(s). S(he) searches for and lists attributes and properties that can be used to distinguish exemplars (of various concepts) from non exemplars. But what s(he) really does is more than just specifying and generalising from different examples that s(he) hears or produces. S(he) is also concerned with identifying and relating the induced examples. Then, s(he) needs to compare different achievements. The efficient way to induce a new own categorisation method in constructivism is to compare a few individuals when their categorical relation(s) is known. Then, s(he) can make her/his personal labels of the concepts categorisation in order to manage and direct different classes of concepts. According to the constructed concepts, the reflection of the prior knowledge (what has been acquired or created before interacting) and the new knowledge (what is being acquired or created during the interaction) and the initial definitions must be negotiated. So, the sequence ‘Prior Knowledge → Definition → New Knowledge’ supports the learner in searching for the initiative meanings of the class/classes of constructed concepts and their relationships, see ‘Search for Meaning’ in the Figure 1. This phase is highly affected by Semantic Interpretation. In fact, initiative meanings are being interpreted in order to be balanced, see Figure 1. From the logical point of view, the interpretation of a defined constructed concept is a function. This function has turned a ‘definition’ into a ‘meaning’. Formally: Interpretation: Definition → Meaning. The Interpretation functions operate the person’s definitions based on her/his constructed concepts. Therefore, they ’activate’ the meanings. This transformation has been presented as Semantic Interpretation in Figure 1. Accordingly, concerning ‘Interpretation: Definition → Meaning’, the definition could be seen as the product of the inverse of interpretation function (Meaning → Definition). Logically, we have iterative loops between ‘definition’ and ‘meaning’. The agent could be able to balance and adjust the initial meanings based on the interrelationships between ‘interpretation’ and ‘the inverse of the interpretation’. The conclusions make an appropriate background for verifying the personally found meanings based on personal defined constructed concepts. Therefore, there are many transformations from ‘Search for Meaning’ into ‘Meaning Balancing’ and vice versa. Let me say “a meaning would be given a better shape after checking the balanced definitions based on personal constructed concepts”. The conclusions will formulate meanings, see Meaning Formulation in Figure 1. In this phase the agent formulates the balanced meanings based on the balanced definitions for her/his personal constructed concepts.
5.3
Meaning Production
The formulated meanings will be organised in order to be produced by the agent. Methodologically, any formulated meaning is a basis for providing a meaningful conceptual structure; let me name it Meaningful Conceptual Structuring. The meaningful conceptual structures are all personally formulated based on personal constructed concepts and definitions. On the other hand, the meaningful conceptual structures could induce new formulated meanings on higher conceptual levels and on higher levels of interaction. Furthermore, the new produced formulated meanings are considered as the developed schemata in constructing higher levels of conceptions. Finally, the meaningful conceptual structures support the agent in providing meaningful meanings. The meaningful meanings highly reflect on the constructor and support her/him in proposing the modified schemata on higher conceptual levels and on higher levels of interaction. So, the person has moved through this semantic loop in order to organise her/his personal constructed concepts and construct her/his personal meanings and produce the meaningful comprehensions.
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CONCLUSIONS
Constructivism is a learning philosophy and educational theory of learning that could be known as a proper foundation for modern learning sciences. A learner and her/his mentor, whose insights are
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based on their preconceptions, on personal knowings and on pre-structured knowledge can actively participate in an interaction concerning the framework of constructivism. The most salient aim could be recognised as “constructing the personal knowledge in the context of interaction”. Then the learner and the mentor may have the opportunity to attain a deeper personal comprehension and greater motivation within the universe of discourse.
Fig 1. Meaning Construction in Constructivist Interactions In this research I have focused on the conceptual and the logical analysis of meaning construction in the framework of constructivism and in the context of interaction. My thoughts have been concerned with my own semantics-based framework. My framework considers the agents (learner and mentor) as two intentional participants. It represents a loop that the learner and mentor move through, which organises their personal constructed conceptions in order to construct meanings and produce their individual meaningful comprehensions. I have analysed ‘Definition and Definiteness’, ‘Meaning and Meaningfully’ and ‘Semantic Interpretation’ using Description Logics (DLs), and have employed the results in development of my framework. DLs has been used for analysing the semantics of some concepts and conceptions within my progress. This research has proposed a new scheme for interpretation based on semantics and on interpretation. Obviously, the proposed semantic loop is self-organised and can promote itself on higher conceptual levels and on higher levels of interaction.
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