METAPHORS OF EMOTIONS: TOWARDS A DATA-DRIVEN FORMALIZATION

Formalization of natural language metaphors is a notorious problem in artificial intelligence and in other overlapping domains. It is semantic vagueness that makes metaphors resistant to formulaic or algorithmic descriptions. Great effort has been invested into modeling metaphors computationally but the issue remains methodologically uncertain and needs further research. This paper works on a practical solution to the problem how metaphorical meaning can be represented in a way suitable for computation. The research agenda of this paper is interdisciplinary; it brings together an algebraic heuristic-driven theory for metaphors developed in artificial intelligence and an applied theory of meaning that comes from cognitive linguistics. This agenda postpones theoretical speculation and argument and is solely solution-focused, which contributes to the value of this paper’s attempt to bridge the cognitive science disciplines whose compatibility, though declared, is seldom demonstrated in a piece of practical research. This paper works with metaphors of human emotions that are linguistically manifested in modern English discourse. Emotions by virtue of their ineffability as qualia are rich in metaphorical conceptualizations and serve the research agenda well. This paper in a meaningful way exposes and ranks designated properties of the FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY concepts and arranges these properties into general-purpose ontologies that explicitly specify metaphorically preferred emotion conceptualizations and are good candidates for computation. In prospect, this paper will account for some theoretical aspects of the research and probe the algorithmic and repetitive nature of schemas that license metaphorical expressions in natural language.


Introduction
Metaphor is a natural language phenomenon whose semantic vagueness furnishes its formal representation with considerable methodological uncertainty and guesswork. An algebraic theory that in a rather straightforward manner spells out semantics of natural language metaphors is suggested by  who use many-sorted first-order logic and syntactic generalization in order to compute different types of metaphors, including creative concepts, which is a very non-trivial task for artificial intelligence (hereinafter referred to as AI) (see also . The theory is heuristic-driven; it gives a structural description of the source and target in a metaphor and specifies the connection between these. There has however been left a vacancy in the theory that needs to be closed from outside the AI domain (Gust et al., 2006, p. 116): "What is needed for an appropriate modeling of metaphors is a list of designated properties of the involved concepts. Such a list must contain relevant information concerning possible properties of concepts that can play a role in metaphors. Furthermore, it seems to be reasonable to rank these properties according to their importance. Clearly, this is a purely empirical problem, but it is necessary to get the correct input for the machinery".

Aim, methods, and material
This paper has an interdisciplinary objective to bridge the domains of AI and of cognitive linguistics in a piece of practical research. It aims to suggest a way how the computable input for metaphor might be tailored using the cognitive linguistic methodologies of semantics of lingual networks (see Жаботинська, 2019). The research agenda of this paper postpones theoretical speculation and argument and appears to involve two items that are solely solution-focused (Prof. Dr. phil. Kai-Uwe Kühnberger, personal communication, September 2019). The first item is to expose and rank in a meaningful way the designated (= paradigmatic, or sortal) properties of metaphorical concepts manifested in natural language; the second one is to pertinently arrange these properties in a knowledge representation model suitable for computation. Among the available models of this kind,  place their preferences upon ontologies, which makes an ontology a reasonable pick for this paper as well. The data for analysis in this paper come from a fragment of modern English discourse on human emotion. Because of their metaphorical abundance, emotions answer the purposes of this paper well.

Literature review
This paper treats emotions as basic irreducible intentional reflective states induced in experiencers by external and internal stimuli . Emotions evoke in the array of organismic subsystems immediate and various responses but by their qualia nature are ineffable. Verbal report on emotions is generally metaphorical. This paper sticks to G. Lakoff and M. Johnson's conceptual metaphor theory and understands metaphor as experiencing one concept in terms of another concept, where these concepts are the target and the source respectively with a set of systematic correspondences between them (see  for an overview of the theory). Individual emotions have valence and are characterized as positive, negative, or ambivalent in its terms. Valence is not an intrinsic property of emotions; it is contextually assigned to them in acts of awareness and interpretation. Emotion concepts show to be unevenly distributed within a four-dimensional emotion space  whose scales are valence (positive vs. negative), organismic arousal (passive vs. active), and appraisal of goal relevance (conducive vs. obstructive) and of coping potential (high vs. low control/power). This paper singles out the FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY concepts from the emotion space. These concepts come each from one of the four regions within the space and sit on its opposite poles: FEAR is negative-active, SADNESS is negative-passive, HAPPINESS is positive-active, and RELAXATION/SERENITY is positive-passive, which safeguards for this paper a span over the entire emotion space. The four emotion concepts lend their names to cognitive linguistic analysis and in this paper are exposed as lexical meanings of these names (here and below, see  for an overview of the linguistic terms and their definitions). The analysis is fueled by a direct sample from the British National Corpus. From there, 4000 discourse fragments have been recruited, with the fear, sadness, happiness, and relaxation/serenity English nouns manifesting FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY respectively. The sample was randomly selected; this was a simple random sample for each of the four nouns naming their respective emotion concepts. There are 1000 items in each emotion concept's data set.
Lexical meaning is a mental construal. Representation of lexical meaning is a semantic network structured by a set of schemas. Each set of schemas accommodates a list of designated properties of the respective emotion concept. These properties capture the intensional definition of the concept. Each schema in a set highlights a distinct designated property and has a different iteration rate in the data. This rate indicates how prominent a property is; prominence distinguishes cognitively preferred designated properties and is a way of their ranking.
Semantic networks for FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY are treated in this paper as structures of ontological knowledge about respective emotions. This knowledge is common-sense, naïve, and non-specialist. However, it is this very knowledge that is crucial for computing natural language metaphors . Ontologies for FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY hold their concepts' designated properties in their relations and allow interpretation and extraction of knowledge about respective emotions.
With this in mind, I give the intensional definitions for FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY in Subsection 2.1 of this paper, and lay the respective ontologies open in Subsection 2.2. Section 3 is a conclusion to this paper and an outline of prospects for further research.

Results and discussion 2.1 Intensional definitions for the FEAR, SADNESS, HAPPINESS, and RELAXATION/ SERENITY emotion concepts
From the AI perspective, mapping between the structured target and source in a metaphor produces a set of systematic semantic correspondences, which is captured by a schema and stored as an abstracting generalization. It is this generalization that is computed once at hand . Schemas define attributes and relations on conceptual entities. Schema is a generalized knowledge structure; the term is of wide application across many scientific domains where it has a more or less shared understanding. In cognitive linguistic view, schemas "can be used to produce and understand linguistic expressions. Linguistic expressions are categorized by schemas in production and comprehension; in other words, they are licensed to occur by those schemas. In this way expressions are linked to the knowledge structures that produce them and make them interpretable" (Kemmer, 2003, p. 70). Schematic representations enable data extraction, data interpretation, and learning in both human and artificial agents .
Intensional definitions for FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY prove largely metaphorical because of ineffability of emotion qualia per se. Each schema in the definition captures a particular (metaphorical) conceptualization of the emotion. In the mappings, information from various source concepts is transferred to the targets and hypothetical world Iteration rates guide the distribution of designated properties into the intension or into the implication of meaning of respective emotion names. Properties in the intension of meaning are stable, formative, and obligatory for this emotion concept by virtue of its name. Intensions are distilled into dictionaries as the signified meanings of words. The implication of meaning embraces unstable properties distributed into different regions: the strict implication includes the most probable associates of the intension but their absence however does not rule the concept out of its category; properties in the weak implication are free, their association with the intension is equally probable or improbable depending on the grounds of categorization. Strict and weak implications are fuzzy sets of properties. Whereas the intension of meaning results from constructivization of reality and is a deterministic abstraction from the infinity of referents and their relations, the implication of meaning reflects the probable, indeterministic nature of the world (see Никитин, 2007, pp. 102-135). Each emotion name therefore carries in its meaning an obligatory and invariable semantic core and an optional and variable periphery of an infinite size. Levels of generalization to which the periphery is pruned depend on particular research objectives and are generally common-sense.
In this paper, distribution of the designated properties of emotion concepts into the intension and various regions of the implication is conditioned by prominence that is measured quantitatively. The intension and implication are peculiarly boldfaced in the definitions; the numerical thresholds for the strict, highly probable, and weak implication are arbitrary with reference to the size of the data set. The thresholds are the following: the signified and the intension of meaning strict implication -more than 50 linguistic expressions that are licensed by a schema, highly probable implication -20-50 expressions, weak implication -less than 20 expressions.
The data set has been formed, systematized, and analyzed. Based on this analysis, for each of the emotion concepts an intensional definition is suggested that captures the designated properties for this concept ranked and marked according to their prominence. Represented as [a numerical value] in the definitions is the number of linguistic expressions that manifest respective properties. The intensional definitions for the emotion concepts are given below:  Sadness can drive experiencers towards certain intentions, and is the cause for action [3]. Sadness accompanies certain states, processes, and actions or is, although infrequently, absent from them [63]; it may also be used to trigger these in experiencers [14]. Sadness can be brought to experiencers, caused or evoked in them; experiencers can be moved to sadness, and sadness can be born from knowledge or can result from the need that humans naturally have for it [17]. Experiencers can act upon their sadness [45] sharing it with others, knowing, remembering, measuring, sorting out, capturing, confronting, relieving, controlling, easing, complicating, and stopping it; they can attach sadness to something, think of their sadness and describe it verbally, can replace sadness with another, positive or negative, emotion that outweighs it.  Relaxation/serenity drives experiencers towards certain intentions, and is the cause for their action [1]. Relaxation/serenity can accompany certain states, processes, and actions or be absent from them [13]. Experiencers can act upon relaxation/serenity [22] completing, increasing and enhancing it, concentrating on and learning it, permitting and affecting it, shattering, threatening or disturbing it. They can also use relaxation/serenity as a means to achieve certain goals [3].

Relaxation/serenity is an emotion evaluated as a positive one [22
These intensional definitions read as narratives, which makes them good candidates for computational storytelling, and adds practical value to this paper although the subject is outside of the scope of research. Intensional definitions comprise those designated properties of emotion concepts that formalization of metaphors ultimately seeks. The definitions are to be represented at the ontological level now.

Ontologies for FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY
An ontology is a knowledge engineering artifact that specifies objects/concepts with their attributes and relations within a domain . Representing these domains is called ontological engineering. There are a number of ways to construct and populate ontologies, the choice depending on particular research objectives. Figures 1, 2, 3, and 4 below set the relevant common-sense knowledge about FEAR, SADNESS, HAPPINESS, and RELAXATION/SERENITY in ontologies. These are general-purpose ontologies that organize and hold together the various specific fragments of knowledge about the emotions. The facts that the ontologies contain are generally translatable into formal ontology language for AI.  ephemeral, great, everlasting, unlooked-for, spiritual, true, Christian, transforming, moderate, hightech, extreme, short-term, lost, unique, special, perfect, mild, fatal, childlike, real, corrupted, sudden, vain   By way of different colors, the figures show relations between concepts within the ontologies and their prominence. These ontologies are explicit specifications of conceptualization for the emotions of fear, sadness, happiness, and relaxation/serenity in the British worldview.

Conclusions and further research
This paper has attempted to bring cognitive linguistics and AI together in an interdisciplinary study of metaphor. It has used big corpus data and trusted cognitive linguistic tools to expose and rank designated properties of major emotion concepts and to arrange these properties into general-purpose ontologies. As explicit specifications of metaphorically preferred emotion conceptualizations, the ontologies that this paper suggests make good candidates for computation in ontology languages for AI.
The research agenda of this paper has been practical and solution-based, with some theoretical issues postponed. One of these issues is metaphor itself with regards to where it is to be terminologically located within the proposed methodological framework. In other words, what conceptual entity exactly is to be considered and termed a metaphor here? Emotions by virtue of their ineffability as qualia are conceptualized metaphorically, and this paper has been clearly operating on metaphors that conceptualize the emotions of fear, sadness, happiness, and relaxation/serenity. The practical value of the solution that this paper suggests for AI does not depend on terminological speculations, still the proper location for the term "metaphor" in the framework will make this solution theoretically immune.
Semantics of lingual networks (Жаботинська, 2019) that this paper adopts is a theory of meaning inspired by frame semantics. The theory, to the best of my knowledge, reserves for metaphor one schema only. It is the comparison likeness schema "SMB/SMTH is as if SMB/SMTH-A CORRELATE" that is assumed to license metaphorical expressions in natural language. In this light, linguistic manifestations that need to be exclusively considered metaphorical for HAPPINESS, for example, are only those 166 expressions in the data set that are licensed to occur by the schema "HAPPINESS is as if SMB/SMTH-A CORRELATE", e.g., happiness is paper-thin, where the mode is fictitious (the wordage for the mode is by Immanuel Kant). However, the mode is equally fictitious for such expressions in the data set as money gives them happiness (the HAPPINESS is A PHYSICAL OBJECT metaphor), there is so much happiness in the community (the HAPPINESS is CONTENT INSIDE A CONTAINER metaphor), etc. These expressions are licensed to occur by other schemas but are metaphorical (at least in terms of the conceptual metaphor theory in its standard version, see  for an overview), which overrides the initial expectation. Cf. also: these other schemas license non-metaphorical expressions, e.g., the teacher gives them a book and there is so much water in the vase; these expressions manifest concrete concepts, and indeed the mode here is actual. Therefore, for abstract concepts like HAPPINESS a lot more schemas need to be treated as those that license metaphorical expressions but not the comparison likeness schema alone, which generally has been shown by this paper's data set.
There is another issue in this train of thought. Could schemas be termed metaphors if they are conceptual structures that license metaphorical expressions? From the conceptual metaphor theory perspective, the answer is presumably yes, although this does not resonate with the methodology and is counter-intuitive. The theory naturally and traditionally handles metaphorical concepts but not metaphorical schemas. Yet, schemas do have their say in the mind's operation, and there are opinions that schematicity interlaces metaphorical concepts and is their central property (see . This schematicity is that of the metaphorical sources that can come from different levels of abstraction and thus be of different degrees of schematicity, e.g., HAPPINESS is A PRECIOUS POSSESSION and HAPPINESS is A JEWEL. Should then the HAPPINESS is A PRECIOUS POSSESSION metaphorical concept be considered less schematic than the "OW owner has OD owned -HAPPINESS" schema? This however is an implausible juxtaposition of entities of different order. Therefore, the terminological refinement for this paper, if aimed at, requires a deeper insight into methodologies and is a prospect for further research. Another research opportunity is the algorithmic and repetitive nature of schemas that license metaphorical expressions for the emotion concepts. There are schools of thought in AI that with the purpose of computation explore productive aspects of metaphors and of creative metaphors in particular. The intensional definitions and ontologies from this paper make valid input for a metaphor generator. Potential metaphorizations of fear, sadness, happiness, and relaxation/serenity are infinite, which is generally the case for any metaphorization thinkable until combinatorial explosion (Prof. Dr. phil. Kai-Uwe Kühnberger, personal communication, September 2019), and what this paper has achieved is cataloguing the regularities of these combinations.