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Copyright © 2006, Lawrence Erlbaum Associates, Inc.
Cognitive Semantics and Spatio-Temporal Ontologies
Werner Kuhn
University of Münster
Martin Raubal
University of California at Santa Barbara
Peter Gärdenfors
Lund University
Cognitive semantics has established close ties between semantics and spatial
cognition. Yet, applications of cognitive semantics to the design of spatio-
temporal ontologies remain difficult and rare. Ideas such as image schemas,
prototypes and radial categories, basic level categories, mental spaces, and
conceptual blendings are still largely unexplored in their potential for ontology
engineering. The only idea that has received wide-spread attention in the
ontology community so far is that of conceptual spaces (Gärdenfors, 2001).
The following special issue presents work at the intersection of several lively
research areas contributing to ontology engineering. It originates in a workshop
on the Potential of Cognitive Semantics for Ontologies that was held in
conjunction with FOIS 2004, the International Conference on Formal Ontology
in Information Systems ( A substantial part of
the workshop contributions addressed the role of space and time, either as
shaping cognition or as subjects of ontologies. The call for papers to this special
issue built on the workshop contributions, discussions, and results
(, but was open to any submissions
on the role of cognitive semantics in ontologies of space and time. Fourteen
papers have been submitted and each of them has been refereed by at least three
internationally renowned scientists. Of the selected four papers, two were
written by workshop participants and two were contributed by others. This
introductory section provides a broader introductory perspective on the topic and
relates the four papers to it.
To motivate research in this area, one might provocatively ask whether
information system ontologies, as used in the semantic web and elsewhere, have
anything to do with meaning. Or, more specifically, where do the predicates
formalized in ontology languages such as OWL (the web ontology language, get their meaning from (Gärdenfors 2004)?
Formal semantics treats meanings of symbols in a language as mathematical
objects (typically as sets). Yet, semantics, no matter what formalisms are applied
to it, is a cognitive phenomenon: it refers to the meaning that symbols have for
human beings. It is determined by individual and cultural factors, involving
human minds anchored in a spatio-temporal world and constrained by the
conventions of a language or information community. This basic position about
semantics is best captured by the saying that “words don’t mean, people do”.
Since mental interpretations and community conventions are typically
inaccessible, ontology engineers face the problem of capturing enough of the
cognitive and social contexts of information in their formalizations. However,
current information system ontologies typically explain predicates in terms of
more abstract, rather than more meaningful symbols. It is essential that ontology
systems assign the same meanings to the symbols as their users do, or provide
the necessary transformation mechanisms, lest they will be unusable. So, how do
the symbols become meaningful?
Tenets of Cognitive Semantics
Cognitive semantics is asking similar questions for natural languages as well as
for symbol systems in general. It studies, among other issues, what the
embodied nature of language can tell us about how human minds construct
meanings, or what the socially situated nature of language suggests as social
mechanisms and constraints on the use and development of concepts and
languages. Some core ideas characterizing a cognitive approach to semantics
Meaning is conceptualization in a cognitive model (not truth conditions in
possible worlds). A semantics for a language is seen as a mapping from the
expressions of the language to some cognitive or mental entities. A consequence
of the cognitivist position that puts it in conflict with many other semantic
theories is that no form of truth conditions of an expression is necessary to
determine its meaning. The truth of expressions is considered to be secondary
since truth concerns the relation between a cognitive structure and the world. To
put it tersely: Meaning comes before truth.
Cognitive models are mainly perceptually determined (meaning is not
independent of perception). Since the cognitive structures are connected to our
perceptual mechanisms, directly or indirectly, it follows that meanings are, at
least partly, perceptually grounded. This, again, is in contrast to traditional
realist versions of semantics that claim that since meaning is a mapping between
the language and the external world (or several worlds or formal models of
them), meaning has nothing to do with perception.
Semantic elements are based on spatial or topological objects (not symbols
that can be concatenated according to some system of rules). The mental
structures applied in cognitive semantics are the meanings of the linguistic
idioms; there is no further step of translating conceptual structure to something
outside the mind. The conceptual schemes that are used to represent meanings
are often based on geometric or spatial constructions. The most important
semantic structure in cognitive semantics is that of an image schema. Image
schemas have an inherent spatial structure. Most image schemas are closely
connected to kinesthetic experiences (Johnson 1987). This also relates them to
the notion of affordances (Gibson, 1977), that is, to perceivable ways that the
environment offers us to experience it.
Cognitive models are primarily image-schematic (not propositional). Image
schemas are transformed by metaphoric and metonymic operations (which are
treated as exceptional features in the traditional view). Metaphors and
metonymies have been notoriously difficult to handle within traditional semantic
theories. In contrast, they are given key positions within cognitive semantics.
Not only poetic metaphors but also everyday creative and 'dead' metaphors are
seen as central semantic features and are given systematic analyses. They are
analyzed as transformations of image schemas. As such they are connected to
spatial codings of information. In particular, Lakoff (1987, p. 283) puts forward
what he calls the 'spatialization of form hypothesis' which says that conceptual
forms are understood in terms of spatial image schemas plus a metaphorical
mapping. Furthermore, Lakoff’s (1990) ‘invariance hypothesis’ suggests that
image schemas are the structures left invariant in metaphorical and metonymic
mappings. More recent work generalizes these notions to mental spaces and
blendings (Fauconnier & Turner, 2002), offering a more powerful and precise
framework for conceptual mappings.
Concepts show prototype effects (instead of following the Aristotelian
paradigm based on necessary and sufficient conditions). The classical account
of concepts within philosophy is Aristotle's theory of necessary and sufficient
conditions. As a result of a growing dissatisfaction with this theory, an
alternative theory was developed within cognitive psychology (Rosch 1978).
This is the so-called prototype theory where the main idea is that within a
category of objects, like those instantiating a property, certain members are
judged to be more representative of the category than others. For example,
robins are judged to be more representative of the category 'bird' than are ravens,
penguins and emus; and desk chairs are more typical instances of the category
'chair' than rocking chairs, deck chairs, and beanbag chairs. The most
representative members of a category are called prototypical members.
Another thesis of prototype theory is that categories are not organized just in
terms of simple taxonomic hierarchies. Instead, a 'middle' kind of concepts can
be distinguished, which is called the basic level of the categorization. Higher
levels are called superordinate and lower subordinate. For example, 'chair' and
'dog' are basic level concepts, while 'furniture' and 'mammal' are superordinate
concepts and 'armchair' and 'dachshund' are subordinate. Within cognitive
semantics, one attempts to account for prototype effects of concepts. A concept
is often represented in the form of an image schema and such schemas can show
variations just like birds and chairs. This kind of phenomenon is extremely
difficult to model using traditional symbolic structures.
The foundation for human categorization are similarity judgments, not lists of
necessary and sufficient features. Consequently, the definition of similarity
measures (Tversky, 1977) becomes central to the construction and use of
ontologies. Similarity notions range from purely syntactic ones (based on
alphabetical “distances”) to complex, cognitively more plausible proposals.
With such a long list of widely researched cognitive approaches to semantics,
how can it be that there is only sparse work on information system ontologies
taking any of these notions seriously, and even less that formalizes and applies
them fruitfully?
Why Cognitive Semantics Matters for Ontology
Since all information is ultimately for and from human beings, its semantics
needs to relate to meanings in human minds. These meanings have observable
effects, primarily in the form of actions in the world resulting from
understanding. Current notions of meaning applied to ontology emphasize realist
semantics (where phenomena in the world are considered to be the meaning of
expressions) over cognitive semantics (where meaning is a psychological
phenomenon, based on phenomena in the world) and situated embodiment
(where meaning also involves the social settings of language use). The
workshop and this special issue were motivated by a desire to balance and
integrate these notions of meaning and work toward more powerful theories of
meaning in support of ontology engineering.
Some core questions unifying the work of interest at this intersection of
cognitive and information sciences are:
1. How do formal models of semantics (e.g., in the Semantic Web) become
meaningful for humans?
2. Do space and time play a special role in explaining and representing
3. What is special about spatio-temporal ontologies from a cognitive
semantics perspective?
4. What kind of formalisms best capture what ideas from cognitive
Expected Benefits to Ontology Engineering
As editors of this issue and researchers having worked on such questions for
many years, we see a number of specific ways in which ontology and ontology
engineering, particularly for spatio-temporal applications, is to gain from
cognitive semantics. Among them are the following:
Grounding ontologies, that is, establishing primitives that are both
meaningful and suitable as building blocks for ontologies. Whether these
primitives are entities, processes, qualities, combinations of these, or yet
something else remains to be seen, but cognitive semantics notions offer
some candidates (Kuhn 2005).
Moving space and time from their current status as application domains to
become foundational aspects of ontology. The findings about the
strongly spatial and dynamic nature of human conceptualizations,
particularly of abstract domains, suggest a much stronger role for space
and time than they currently have.
Moving ontologies from their predominantly static nature to a stronger
process-orientation (Grenon & Smith, 2004; Raubal & Kuhn, 2004).
Cognition is increasingly recognized as being shaped by process and
action much more than by static structure. Many of the cognitive
semantics notions listed above have a dynamic flavor, even if they are
still too often described and formalized statically.
Reconciling meaning and truth. Realist semantics has established a
notion of meaning that is entirely based on truth (of sentences in some
formal models). Cognitive semantics, on the other hand, has sometimes
lost sight of observable, hard facts and shared reality when studying
individual cognitive phenomena. While it remains a puzzle how one can
establish truth without meaning, the ideas of embodiment and
situatedness provide strong and dynamic links between the two.
Allowing for perspectivalism in ontology, without giving in to relativism.
It is primarily spatial domains which show how important it is to admit
multiple perspectives on reality, e.g. in the form of multiple granularities
(Bittner & Smith, 2001) or as dependent on the context. However, these
perspectives are linked by and grounded in some fundamental properties
of the world and of human cognition.
A cognitively plausible or even adequate understanding and formalization
of conceptual mappings. Metaphor and blending theories have revealed a
great deal about the ways concepts get mapped within and across
domains. They have also shown striking parallels with notions in
mathematical category theory, offering powerful support for
formalizations of mappings. Applications to ontology mappings in
spatio-temporal domains can furthermore benefit from an analogy to
spatio-temporal reference systems (Kuhn, 2003).
A sound theory of conceptual mappings would lead directly to an
enhancement of human-computer interaction: Communication between
systems and their users is made possible through the mutual
understanding of terms and concepts. If we want geospatial services and
tools to give better answers to user queries it is necessary to bridge and
eventually resolve the discrepancy between user concepts and system
concepts. By applying and utilizing conceptual mappings it will be
possible for a system to adapt the semantics of its concepts to the user’s
semantics, which eventually leads to improved human-computer
interaction (Raubal 2004).
Personalizing geospatial services: People’s information needs depend on
situational and personal context. In order to find both useful and usable
solutions to people’s geospatial problems it is therefore essential to
consider diverse concepts, cognitive and spatial abilities, and strategies
during the problem-solving process. A cognitive semantics approach to
designing spatio-temporal ontologies underlying these geospatial services
accounts for the fact that different people have different
conceptualizations of the world and therefore require different answers
and presentations of answers to their spatio-temporal questions.
While this list is surely not exhaustive, and shaped by our own work and
interests, it should convey the appeal of cognitive approaches also to those who
have not yet considered them or struggle with problems to which they might
contribute solutions.
The Contributions in This Issue
The special issue presents a snapshot of ongoing work in this direction, rather
than a compendium of achievements. It is primarily meant as an incentive to
initiate more work at this fruitful intersection of engineering, computing,
mathematics, ontology, and cognition. The four papers following this
introduction share the general spirit of bringing information system semantics
closer to human cognition, and making ontologies more powerful. They cover a
broad spectrum of ideas, ranging from specific cognitive notions and their
formalization as upper level ontological categories through empirical work on
concept formation and evolution, to more powerful mathematical approaches to
deal with mappings between different conceptualizations.
Kai-Uwe Carstensen, in Spatio-temporal Ontologies and Attention, proposes
to use attentional patterns as upper level categories for spatio-temporal
ontologies. Attention produces explicit and unique spatial relations, where the
objective configuration of objects would allow for multiple descriptions. For
example, by shifting our attention from a table (with many implicit relations to
objects on it or surrounding it) and zooming to a specific cup on it, we establish
a “microperspective” that generates explicit figure-ground (or trajector-
landmark) relations, allowing us to say (and to understand) that “the cup is on
the table.” A dominant factor in such attentional selections is boundedness, both
in space and time. Carstensen sketches upper level ontological distinctions for
entities (including objects, masses, events and processes, but excluding qualities
and abstractions), based on attentional criteria. The innovation and motivation of
this work lies in a treatment of spatial relations that is based on attentional shifts
rather than on static geometry or on function. It accounts for both linguistic data
and recent evidence on cognitive spatial relation processing. The implications of
Carstensen´s approach are potentially even broader: by highlighting the
representational aspects of selective attention patterns, it also presents new
criteria for the design of cognitively motivated ontologies, and sheds a new light
on cross-domain relationships, e.g., in linguistic metaphors.
Olav K. Wiegand proposes A Formalism Supplementing Cognitive Semantics
Based on Mereology. He focuses on the notion of Gestalt, which has a long
history of influencing spatio-temporal theories. The structuring of entities into
structures of parts depends on the perspective taken by an observer and therefore
calls for cognitive theories. Mereology, which studies part-whole relationships,
is therefore one of the areas where logical theories are already being applied to
cognitive phenomena. Wiegand goes beyond standard mereological theories and
formalizes Gestalts as structured wholes, capturing the interdependence of parts
and the context of a certain part-whole relationship. He introduces R-structured
wholes as a solution to the vexing question whether part-whole relations are
transitive (i.e., whether John’s nose is part of the Berlin Philharmonic if John is).
An elementary language to describe R-structured wholes is being proposed, with
the goal to support reasoning about Gestalts, where reasoning is understood as a
sequence of cognitive transformations.
In Experiments To Examine The Situated Nature of Geoscientific Concepts,
Brodaric and Gahegan provide empirical evidence from geological fieldwork for
several ideas in cognitive semantics. In particular, they supply strong support to
their own idea of “situated concepts”, i.e., concepts like Dakota Sandstone,
which are more specific than domain universals (Sandstone), but more general
than individuals (Dakota). The specificity may stem from a regional context, but
also from other natural, scientific, or human situations, such as a historical
context or a new theoretical insight. The generality is important to highlight the
categorizing effect of such concepts, distinguishing them from a pure instance
labeling. Interestingly, situated concepts depend on actual process instances,
rather than on process types, distinguishing them from affordance-related ideas.
Situated concepts are necessarily context-dependent; their origin may depend on
examples encountered first, and they can evolve over time within a process.
Thus, incorporating them into ontologies is a promising way to more dynamic
theories of meaning. Through a detailed statistical analysis of clusters in a
conceptual space representation, the authors are able to identify and distinguish
the influences of field observations, domain theories, and physical or human
situations on concept formation and evolution in geological fieldwork. An
implication of their results for formal ontology is that meaning representation
for some concepts would seem to require representation of their situational
Admitting multiple perspectives on space-time raises the question of how to
combine them. John Bateman, Stefano Borgo, Klaus Lüttich, Claudio Masolo,
and Till Mossakowski address this question in their study of Ontological
Modularity and Spatial Diversity. The challenge is to select a foundational
ontology that does not impose a particular view of space, and a specification
mechanism for mappings (morphisms) between multiple ontologies. The authors
identify DOLCE as the only foundational ontology allowing for alternative
views of space and qualities. Combining it with CASL as an algebraic
specification language, they establish a general mechanism for relating modular
ontologies and formalizing theory morphisms between them. A standard
software engineering technique has, thus, found its way into ontology
engineering, and promises the well known benefits of modularity in terms of
reuse, refinement, and complexity reduction. The authors introduce the central
notion of a view (from CASL) to map from one ontological specification to
another. They apply their method to a spatial example involving two graph
conceptualizations of space (as a transportation network and as a route graph), a
region conceptualization (for sections of a town), a qualitative distance notion
and simple physical qualities such as color. With the natural inclusion of type
and token level knowledge in their specification, it becomes possible to express
queries (or, in their case, wayfinding instructions) as theorems to be proven by
using multiple logical theories. Their formalization approach also captures the
cognitive notion of conceptual blends and should therefore offer great power to
capture many cognitive semantics phenomena, especially those arising in
information integration.
We sincerely acknowledge the great efforts from the submitting authors, and the
dedicated help from the reviewers. The participants of the workshop at FOIS
2004 gave us the confidence that the topic warrants follow-up activities like this
issue. Too many colleagues and friends to name individually have encouraged,
accompanied, taken up, and, most importantly, criticized our work in this area.
List of Reviewers
The following colleagues wrote very helpful reviews for one or more
submissions to this issue: Ola Ahlqvist, Michel Aurnague, John Bateman, Mike
Batty, Melissa Bowerman, Gilberto Câmara, Helen Couclelis, Matt Duckham,
Fred Fonseca, Andrew Frank, Mirjam Fried, Antony Galton, Aldo Gangemi, Pat
Hayes, Jerry Hobbs, Kim Kastens, Marinos Kavouras, Bernd Krieg-Brückner,
Benjamin Kuipers, Ron Langacker, David Mark, Claudio Masolo, Dan
Montello, Barry Smith, John Stell, Laure Vieu, Anna Wierzbicka, Stephan
Winter, Michael Worboys. Additional reviewing comments were provided by
Frank Dylla, Krzysztof Janowicz, Till Mossakowski, Florian Probst.
This special issue is dedicated to Joseph Goguen, formerly Professor in the
Department of Computer Science and Engineering, University of California at
San Diego. He inspired the work that led to the issue, back in 2003, when he
suggested organizing a workshop on cognitive approaches to spatial semantics.
He then participated at the FOIS workshop as a keynote presenter and active
discussant. Though he was planning to submit a manuscript to this issue (on
modeling image schemas using nonlinear dynamical systems theory), his health
did not permit this. In July 2006, Joseph passed away. He leaves us with an
immense range of profound contributions to many areas of science and the arts -
and with the obligation and inspiration to carry on.
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... As mentioned by Kuhn, Raubal, and Gardenfors (2007), applying cognitive semantics in the design of spatio-temporal ontologies remains a challenge. The conceptual spaces defined by Gärdenfors (2000Gärdenfors ( , 2014 have been widely adopted. ...
... However, to our knowledge, other cognitive concepts such as image schemas and concept blending have not been yet applied to ontology engineering. Kuhn, Raubal, and Gardenfors (2007) underlined that, in order to be more cognitive, geospatial ontologies should: ...
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... R.Hung 2010;Foreman et al. 2005;Rainville et al. 2005;Kuipers et al. 2003;N. Gale et al. 1990). Where semantic meaning plays a role in most spatial learning(Hecht and Raubal 2008;W. Kuhn et al. 2007;Bolte and Goschke 2005;W. Kuhn 2002; Kuipers 2000), be it about the context or factors outside of the immediately available environment, exploration can be considered as naturally roaming a place without superstructure beliefs like culture or personal background guiding normative behavior in unfamiliar contexts(Haun et al. 2011;Henrich a ...
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This thesis is an attempt to integrate contending cognitive approaches to modeling wayfinding behavior. The primary goal is to create a plausible model for exploration tasks within indoor environments. This conceptual model can be extended for practical applications in the design, planning, and social sciences. Using empirical evidence a cognitive schema is designed that accounts for perceptual and behavioral preferences in pedestrian navigation. Using this created schema, as a guiding framework, the use of network analysis and space syntax act as a computational methods to simulate human exploration wayfinding in unfamiliar indoor environments. The conceptual model provided is then implemented in two ways. First of which is by updating an existing agent-based modeling software directly. The second means of deploying the model is using a spatial interaction model that distributed visual attraction and movement permeability across a graph-representation of building floor plans.
... Radionica "Potential of Cognitive Semantics for Ontologies" (Kuhn et al. 2006) u okviru me|unarodne konferencije FOIS 2004 7 jedan je od najboljih primjera organizirane aktivnosti interdisplinarne znanstvene zajednice usmjerene prema kombiniranju formalnih i kognitivnofunkcionalisti~kih pristupa u oblikovanju ra~unalnih ontologija kojima se uzimaju u obzir temeljna na~ela kognitivne semantike. Dakako da pritom velik problem predstavlja ~injenica da ra~unalu nisu direktno dostupne umne reprezentacije i dru{tvene i kulturolo{ke konvencije (ibid.), ...
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It is argued that an interdisciplinary approach to description of linguistic phenomena combining formal and cognitive linguistic theories provides a foundation for a research and scientific platform greatly facilitating exchange of valuable specific knowledge, benefitting different involved scientific domains, in this case computer science and cognitive linguistics. This paper proposes a means of introducing formal methods for assessing the level of representativeness within the frame of the prototype theory of cognitive semantics. The methodology and terminology are taken from fuzzy logic theory and linear algebra. A model is proposed wherein categories are represented as fuzzy sets containing concepts. Their membership is not of binary character as proposed by radical structural semantics; instead, it is quantitified by concepts’ properties which contribute in various amounts to their representativeness within the pertaining categories. For each property of a concept a function needs to be defined by which the contribution of the property to the membership to the fuzzy set is quantified. The proposed model posits concept representativeness as a vector within a vector space such that each space dimension corresponds to one property. Coefficients along basis vectors that span this vector space comprise the weight factor of the pertaining property and the value of the function quantifying the membership of the concept to the category with respect to that property. Furthermore, the paper proposes the application of the described model to complex semantic structures. The representativeness of a situation within the pertaining situation category is a vector in of a vector space space spanned by basis vectors which in this case correspond to concepts constituting the complex semantic structure. Situation representativeness is a function of selection restrictions posited to each constituting concept by other concepts within the same complex semantic structure and representativeness of each concept within its category if observed isolatedly. After offering the description of the quantification model, it is argued that such a model may provide a basis for the improvement of existing or devising of new computer systems for natural language processing by implementing the principles of categorisation undisputedly present within the cognitive processes. Finally, areas for further research and improvements are suggested.
Geographers describe, predict, and explain human activity on the Earth. The concept of spatial behavior highlights the geographer's focus on the spatial and temporal aspects of this activity. An important way to understand spatial behavior is to understand the human thought and reasoning partially underlying it, including the subjective mental representations that people have about the world and themselves. This is known as cognitive geography. After reviewing basic concepts of cognition and empirical methods for studying cognition and spatial behavior, this entry discusses concepts, theories, and empirical research on cognitive maps and mapping, environmental spatial learning and development, navigation and orientation, distance and direction knowledge, cognition of cartographic maps and other geographic information displays, and natural language and space.
The purpose of this paper is to present an approach to develop ontology based applications for semantic web using OWL [9] ontologies derived UML [19]. Description logic based ontology languages such as OWL are usually defined in terms of an abstract (text-based) syntax and most care is spent on the formal semantics. The absence of a visual syntax has lead to propose a particular visual notation for the classic description logic. Conversion from UML to OWL should be done in a very precise way because it is not as straightforward as it seems. It is quite likely that there are multiple alternatives in OWL for representing of elements of the same UML construct and we would probably need best practices for the same. The study will devise a straightforward standard approach for converting UML diagrams to OWL to be used by developing tools to produce an ontology based application.
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Information services assist people in their decision-making during the performance of certain tasks. In order to determine if a data source, which commits to a given ontology, can be employed for a service, the service provider needs to evaluate its usability and utility for the decision-making process. We propose to do this by simulating with the ontologies the tasks to be supported by the service. Such a simulation needs to access data about entities based on the actions they afford and the events they participate in. This requires that ontologies include information about these affordances and events. The paper demonstrates a formalized framework, which satisfies this requirement by including functions in the ontologies and making the specifications executable. A real-world scenario for a navigation service—instructions for crossing a river by car—demonstrates the applicability and benefits of the approach in a dynamic scenario.
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We propose a modular ontology of the dynamic features of reality. This amounts, on the one hand, to a purely spatial ontology supporting snapshot views of the world at successive instants of time and, on the other hand, to a purely spatiotemporal ontology of change and process. We argue that dynamic spatial ontology must combine these two distinct types of inventory of the entities and relationships in reality, and we provide characterizations of spatiotemporal reasoning in the light of the interconnections between them.
I view cognitive linguistics as defined by the commitment to characterize the full range of linguistic generalizations while being faithful to empirical discoveries about the nature of the mind/brain. The Invariance Hypothesis is a proposed general principle intended to characterize a broad range or regularities in both our conceptual and linguistic systems. Given that all metaphorical mappings are partial, the Invariance Hypothesis claims that the portion of the source domain structure that is mapped preserves cognitive topology (though, of course, not all the cognitive topology of the source domain need be mapped). Since the cognitive topology of image-schemas determines their inference patterns, the Invariance Hypothesis claims that imagistic reasoning patterns are mapped onto abstract reasoning patterns via metaphorical mappings. It entails that at least some (and perhaps all) abstract reasoning is a metaphorical version of image-based reasoning. The data covered by the Invariance Hypothesis includes the metaphorical understanding of time, states, events, actions, purposes, means, causes, modalities, linear scales, and categories. Because the source domains of these metaphorical concepts are structured by image-schemas, the Invariance Hypothesis suggests that reasoning involving these concepts is fundamentally image-based. This includes the subject matter of Boolean, scalar, modal, temporal, and causal reasoning. These cases cover such a large range of abstract reasoning that the question naturally arises as to whether all abstract human reasoning is a metaphorical version of imagistic reasoning. I see this as a major question for future research in cognitive linguistics.