One of the first developments of cognitive science was that of the http://en.wikipedia.org/wiki/Image_schema¹[¹ Johnson, M. (1987), The Body in the Mind: The Bodily Basis of Meaning, Imagination and Reason., (Chicago: University of Chicago Press).]. An image schema is, in its most basic form, a structured representation of a directly experienced situation as close to how it is experienced as possible. An example of such an image schema is that of a container. We acquire such a schema by our direct experiences, as a child, of containers such as bottles, cups, or our bodies. The container schema has three core elements; an inside, an outside and a boundary. These are sufficient to describe the notion of being a container, or being contained.

The key aspect of a primitive schema is that it is natural (that is, captures a broad generality of experience) and that it is grounded (that is, it is based entirely on direct experience.) It is these properties of image schemas that set apart cognitive approaches to semantics from the previous work on semantic primitives performed by Schenk and Fodor.

Following on from the development of image schemas, was the idea of generalised or http://en.wikipedia.org/wiki/Conceptual_metaphor²[² Lakoff, G. and Johnson, M. (1980), Metaphors we live by, (Chicago: University of Chicago Press).]. Obviously, not everything we conceptualise or express is concrete, however evidence suggests that we treat such abstracts in terms of more concrete schemas. The device that allows this to happen is that of metaphor. A generalised metaphor is a semi-structured mapping between two domains; the source — considered to be the more concrete domain — and the target — considered to be the more abstract.

Each metaphor allows some of our intuitions regarding a concrete experience to be used to tackle an abstract concept. An oft-cited example of a generalised metaphor is ‘LIFE is a JOURNEY’. Following convention, the domains are written all in capitals. The source of this metaphor is the experience of having a journey whilst the target is that of being alive. The inferences which may be drawn based on this metaphor include that of life being of uncertain length, with the possibility of becoming lost and of finding companions along the way. These inferred properties of life are direct analogues of the corresponding parts of the domain of journeys.

Whilst some metaphors are cultural, and exist only for the members of those cultures they’re found in, many are grounded in the property of having a human body. As an example take the metaphor ‘ANGER is HEAT’. This can be seen in such expressions as ‘He’s blown his top’ and ‘burning rage.’ These are not merely arbitrary fancies of language, but based upon the physiological experience of anger as blood flow (and pressure) increases.

Obviously, not every image schema or metaphor will apply exactly to every situation. Lakoff³[³ Lakoff, G. (1987), Women, fire, and dangerous things: what categories reveal about the mind, (Chicago: University of Chicago Press).] proposes the notion of radiality; that is, structuring concepts in terms of other concepts using uncertain links. The idea of radiality grew out of Rosch’s work on prototypes and exemplars in the 1970s⁴[⁴ Rosch, E. (1975), ‘Cognitive representations of semantic categories’, Journal of Experimental Psychology: General, 104 (3), 192—233]. Rosch’s initial experiments involved the naming of colour terms in various languages and cultures. It was found that if two languages were to have the same number of primitive colour terms then they would be the same terms.

This surprising result was extended to more general situations, culminating in Lakoff’s idea of an Idealised Cognitive Model (ICM); an element of a radial conception defined in terms of certain relevant prototypes (intensions) and exemplars (extensions). The key insight is that the meaning of a term is contextual, depending on the currently active prototypes and exemplars to select the most appropriate ICM. One example of such an ICM is that of ‘mother’, which may refer to the woman who gave birth to one, the woman who reared one, the woman who donated the egg for one, etc. The sense of mother chosen is dependent on the discourse context and the state of mind of the understanding agent.

It is important to note that radiality implies an uncertain reasoning process; both non-deterministic and couched in terms of balanceable degrees of belief. The former point is a direct consequence of the context dependence of term understanding, whereby a given term only has meaning in a given situation. The latter is a consequence of the need to balance evidences regarding which prototypes and exemplars are relevant and to what degree — so called blending. Evidently, we need at least a second-order uncertain semantic model and logic in order to describe such reasoning processes.

Humans exist within time. Although that statement is obvious, many logics proposed to formalise human thought are sadly ignorant of it. The human notion of time is the subject of the area of research known as narrative cognition or http://en.wikipedia.org/wiki/Cognitive_rhetoric⁵[⁵ Turner, M. (1998), The Literary Mind: The Origins of Thought and Language, (Oxford, UK: Oxford University Press).]. The key idea is that image schemata may be linked together to form narratives within a domain. These are subject to the same principles of metaphor and radiality as are suggested for working with atemporal schemata. This allows one to understand complex events in terms of simpler, more concrete stories acquired through direct experience.

Narratives may have complex structures including iteration, conditionality and stochasticism. However, no matter how complex an event is, under the cognitive perspective it is understood by its metaphoric relationships to more concrete, directly experienced event frames. These primitive event frames show up in the basic constructions of languages — such as the force-dynamic schemata of Talmy⁶[⁶ Talmy, L. (2000), Toward a Cognitive Semantics, 2 vols. (1; Cambridge, MA: MIT Press).] — but also in the narrative heritage of a culture, such as its parables, fables and fairy tales.

In this essay I have introduced four of the most important elements of cognitive theory at this present time; image schemata, generalised metaphor, radiality and narrative. These, together with the prodigious amounts of experimental evidence being acquired by researchers, put some severe constraints on plausible logics for representing cognitive processes.

A plausible cognitive logic must allow structuring of knowledge in terms of experienced, n-ary relations (image schemata). More abstract concepts must be able to be linked to more concrete ones in a semi-structured fashion (generalized metaphor). In addition, these relations should be at least second-order uncertain and include second-order uncertain inheritance and similarity statements to allow the statement of the prototypes and exemplars of any given relation (radiality). Lastly there must be a (likewise second-order uncertain) temporal aspect to the logic, allowing one to situate the system’s knowledge within time.

Currently, the only system which I’m aware of which meets these criteria in the Non-Axiomatic Reasoning System (NARS) of Wang⁷[⁷ Wang, P. (2006), Rigid Flexibility: The Logic of Intelligence, eds. Gabbay, D. M. and Barwise, J., (Applied Logic Series, 34; New York: Springer).]. It is this system to which I’ll be devoting much of my attention in my coming posts. Watch this space.