Keywords

Introduction

Similar to other computational systems , such as database systems , GIS lacks a sound paradigm and a conceptual model . In contrast to the deep research interests in computational implementations, ontological concerns with spatial information are lacking, which in turn results in a mismatch between the formal model and human spatial cognition and inhibits progress in spatial data handling (Chrisman et al. 1989; Openshaw 1990). In contrast, contemporary linguistics has achieved great successes after flourishing for more than a hundred years. Human beings are approaching an era of ubiquitous machine translation, and natural language understanding lies at the heart of Artificial Intelligence. Contemporary linguistics has implications beyond being a stand-alone discipline: it is becoming a universal methodology that is applied widely in both the natural and social sciences , including such fields as cognitive science , sociology, philosophy, psychology , computer science, and many others. As a major channel of human communication, the progress with linguistics and computers will certainly provide models for automatically addressing geographic information.

A Philosophical Perspective in Theoretical Cartography and GIScience

Cartography has a long history as a science that addresses the representation, communication and exploration of spatial knowledge. Cartography is primarily concerned with map making and map use, and it has evolved considerably since the introduction of computational technologies . GIS first became prevalent in the 1960s and progressed further, into GIScience , around the 1990s. The characteristics of information integration mean that GIS goes far beyond mapmaking or even pure spatial knowledge. However, cartography is still important because spatial knowledge plays an exclusive role in GIS. The two main components of cartography are maps and people, while in GIS, various types of map data (e.g. digital maps , images, attributes, multimedia, etc.), machine components (computers, networks, software ) and people (GIS designers, GIS users , society at large) are the key players. In GIS, machines function to replace aspects such as paper-based recording and to augment human spatial thinking ability. Machines, along with computation technology , prevailed in these aspects and have undergone rapid development for decades; hence, other aspects of cartography have been somehow overlooked and lagged behind.

Traditionally, theoretical cartography has been closely related to different schools of philosophy. In fact, it is difficult to even list all the different philosophical approaches to theoretical cartography . Epistemology is concerned with human cognitive and aesthetic aspects as they relate to map symbols, colours, patterns and layouts. Semiotics is concerned with conceptual model of maps and their surroundings. Metaphysics was also adopted to build a theory of cartography (e.g. meta-cartography), and ontology has also played a role. To date, semiotics seems to prevail in the theoretical cartographic community because it has the ability to both explain and assign value to the methodology . In contrast, ontology is becoming popular in GIScience via information science and knowledge engineering . Philosophical perspectives always dominate in cartographic and GIScience research.

Maps and cartography have a history nearly as ancient as that of humans, while GIS has existed for only the past few decades, and GIScience has an even shorter history. GIScience has learned much from previous efforts in theoretical cartography . To some extent, maps are to GIS as theoretical cartography is to GIScience. The analogy is both meaningful and significant. Cartography addresses not only maps but also map users ; it considers the human mind and cognition . GIScience addresses spatial data associated with geographic meaning and knowledge and involves the ability to process and interpret them. This comparison extends to aspects such as the social space of a map vs. the cyberspace of a geographic information service.

Advances in the Philosophical Aspects of GIScience

Ontology, epistemology and linguistics are three main branches that have developed in philosophy. These aspects represent different approaches for understanding the universe and humanity: ontology is concerned with existence , epistemology with knowledge, and linguistics with existence via knowledge.

Ontology

Ontology is the earliest philosophical branch concerned with being and existence; the general rules and constructs in the universe; the science of what is; the types and structures of objects; and their properties , events, processes and relations in every area of reality . Ontology generally inspires the descriptions of reality , even the representation of reality in our minds (i.e. our conceptualization of the world).

In GIScience , ontology can help in building better models of geographic space, including upper level ontologies, domain ontologies and task ontologies. Ontology is becoming a knowledge framework in information science.

Apart from a universal ontology, ontologies often change from time to time, place to place, domain to domain and task to task. An ontology can be seen as a common communal conceptualization. An ontology cannot be built in an intuitive or empirical way. Cartography can help build better geographic ontologies because a map itself is a conceptual system that represents human cognition of the geographic space at different historical points , cultures , locations and domains and for different purposes. This map spectrum is the sole geographic ontological base represented by map language . To mine geographic ontology from different maps could be a feasible way to build a more intelligent GIS.

Epistemology

Epistemology is related to our cognitive ability and our knowledge system . A mental map is the best result of the epistemological process. Epistemology, in turn, reflects the difficulty of understanding existence when leaving our cognition aside. We look inward to ourselves to determine what we can understand, how we can represent and organize the reality in our mental world. Epistemology is strongly connected with aesthetic and psychological processes.

In GIScience , epistemology is closely related to algorithmic and analytical models. Cartography has a long history of research on human perception and cognition regarding map symbols, colours and spatial patterns, and it is strongly connected with aesthetic and psychological processes. Map creation and map reading are two inverse cognitive processes that encode and decode spatial knowledge, respectively, mediated by cartographic representations . The interaction between a human and map, incorporated based on the geographic circumstances in which the map was made and used, is a perfect model for communicating knowledge.

Linguistics (Semiotics)

In information science, linguistic paradigms play a main role in connecting ontology and epistemology because ontology stems from conceptualization by epistemological processes and requires language to formalize it—i.e. language represents observations of reality (ontology) through the filter of our minds (epistemology). Maps, which are a type of spatial language or semiotic system , have dual functions ; they both record our knowledge about the world and provide knowledge about the world. A map as a cognitive model, as a communication channel, as a spatial index tool and as a spatial analytical tool reflects its linguistic function perfectly. Syntactics, semantics and pragmatics are three aspects of the language system that provide different methodological approaches by which we can perform in-depth investigations of the structure of a language system .

A map archive is a knowledge base that provides not only descriptive knowledge but also declarative and procedural knowledge.

Thus, considering GIS as a linguistic system is a more useful concept than considering it as a database or set of geographic objects. Using a linguistic perspective, GIS will become more structural, meaningful and useful. Numerous linguistic approaches developed over the more than 100-year history of modern linguistics can be applied to geographic data ; these include phonetics , phonology , morphology , syntax, semantics, psycho-linguistics , sociolinguistics, historical linguistics , mathematical linguistics, applied linguistics, visual linguistics and many others.

Various Approaches to Linguistic Paradigms in GIScience

The linguistic paradigm is not new in geographic information-related disciplines . The most important is map language theory, which stemmed from Bertin’s retinal variables (Bertin 1967) and is one of the three most popular cartographic theories. The map language paradigm regards maps as analogues of either natural language or semiotic systems through which the association of content and expression or referent or that of communication and interpreter can be investigated (Blaut 1954; Decay 1970; Schlichtmann 1979, 1985, 1994, 1999; Head 1999). The main concern of this approach regards conceptual models of maps and their digital forms (Schlichtmann 1999).

Another linguistic paradigm approach stems from the viewpoint of cognition , which reaches back to Russell’s idea that the structure of language corresponds somehow to the structure of the objective world. The typical example of this approach was advanced by initiative 2 of NCGIA—a linguistic aspect of spatial relations (Mark 1988, 1991; Mark et al. 1989; Frank and Mark 1991; Mark and Frank 1992; Egenhofer and Shariff 1998).

A third approach that is still popular in disciplines such as pattern recognition and digital image processing and their descendants in cartography and GIS (Youngmann 1978; Taketa 1979; Nyerges 1991; Du 1997, 1998) takes a more methodological viewpoint.

Although linguistic paradigms are widely accepted in geographic information-related circles, a complete and genuine linguistics -oriented investigation is absent, especially from a microcosmic viewpoint. Thus, the research into the linguistic paradigm in this chapter is primarily concerned with methodology at the microcosmic level, which considers the representation of geographic information as an analogy to natural language to construct a phonetic , semantic and syntactic theory of geographic information as a two-dimensional graphic language.

In contemporary linguistics, different schools have their own terminology. However, they do have something in common. The following is the essential acceptance of the language system .

  • A language system is composed of three structures, i.e. phonetics , syntax and semantics. Among these three independent structures, phonetics and semantics are the two ‘poles’ of the symbol unit of language. All language components consist of these two poles.

  • However, the two poles of phonetics and semantics cannot form language components by themselves; they are only the elements of language components. Only when combined by these two elements can language components such as lexical and syntactic components be formed.

  • Lexics and syntax are not two poles; they are two levels of language symbol.

These linguistic principles form the basis for constructing a linguistic system , which is embedded with widely utilized linguistic terminology such as phonetics , semantics, lexics and syntax, and in which each element and component possesses a more complicated internal structure.

Spatial Phonetics and Phonology

In Linguistics , phonetics addresses the physical characteristics of language—the sound in verbal language and the ‘stroke’ of a character in written language . In a graphic representation of geographic information, the physical characteristics are carried by graphic ink strokes rather than sound; thus, research into the physical characteristics of graphics is analogous to a phonetic analysis of a spatial information language.

Physical Characteristics of Geographic Information

In theoretical cartography , concern with the physical characteristics of a map began with Bertin’s retinal variable theory . Many map semiotic and linguistic scholars regard retinal variables as the minimally distinct features (DF) of map symbols.

Dimensionality is another physical characteristic of spatial information . Points , lines, area and volume are four geometrical components with different dimensions. Among these, point s are indivisible, while the others are extended components that can be further subdivided.

As the representation of geographic reality , the appearance of a geographic object is the full presentation of its physical characteristics. In fact, the appearance is dominated by three factors: geographic reality , cognitive restrictions and geometric rules.

Phoneme and Phoneme Combinations in Geographic Information

Phonetic analysis of language is the analysis of language’s physical characteristics through the application of linguistic rules. Although geographic reality has a continuous distribution over space, humans generally tend to discretize the essentially continuous phenomena .

Phonetic syncopation based on retinal variables such as distinctive features is the most important procedure in phonetic analysis. Different syncopation methods stem from different disciplines and have different purposes, among which are geometric and psychological syncopation in pattern recognition, mathematic morphology and cartographic syncopation.

A phoneme is the minimal (and meaningless) phonetic element that functions as a signal that allows the meaning of higher language units to be distinguished. In geographic information, retinal variables and dimensionality have the potential to act as DFs that comprise phoneme-based syncopation. After analysing eight retinal variables, we find that they are still not atomic enough for phonetic analysis, among these, only colour, brightness, size and orientation are truly atomic features . Regarding dimensionality, points and line segments have two different dimensions that cannot be further divided (i.e. dividing a line segment results in two line segments). Thus, we can see that point or line segments with variable colour, brightness, size and orientation form the phonemes of the graphic language system . All other phonetic aspects of the linguistic component are combinations of these phonemes.

The power of graphic symbol expression comes from the various combinations of the phonemes, as well as allophones of a given phoneme. Combining these phonemes results in minimal meaningful units (morphemes) or in still-meaningless units (syllables). In the context of geographic information, creating phoneme combinations has traditionally been the domain of map symbol design .

Suprasegmental Phonemes in Geographic Information

Just as the characteristics of phonetics underly the entire speech stream in natural language, the graphic characteristics of spatial information are reflected in the entire distribution pattern. After a morpheme is constructed that can carry certain semantics, general phonetic analyses at the levels of morphemes, words, phrases or sentences is the task of suprasegmental phonology . Here, geographic reality and its conceptual system take the position of geometrical rules as the main functional factors. For example, the curve of a line or a minimal simple polygon of an area could be suprasegmental phonemes.

Spatial Semantics

Semantics addresses the meaning of language , and in geographic information, the semantics lie in the association of geographic information and geographic reality . Two main semantic theories exist, one of which is concerned with the semantics within the language system (i.e. how words and sentences are mutually connected) and the other with semantics outside of the language system (i.e. how words and sentences are connected with their referent objects and processes).

Component Analysis of Semantics in Geographic Information

A component analysis of spatial information involves decomposing the ‘meaning’ into ‘semantic features’, in other words, the analysis of the internal semantic features that reflect the objective essence by an empirical understanding of geographic features and phenomena . The inner semantic features are independent of a concrete language context ; they are associated with the ontology of reality that the words express.

Thus far, in linguistics , an efficient theory for semantic feature extraction is lacking: empiricism and introspection are two main approaches. Regarding geographic information, the corresponding geographic ontology is much confined in comparison with the reality corresponding to natural language ; thus ontological investigation is an efficient approach.

Borgo et al. (1996) and Guarino (1997) proposed the concept of ‘Ontological Strata’ (Fig. 3.1) for the construction of large-scale ontologies. ‘Objects have an intentional criterion of identity , in the sense that they are more than mere sums of parts . Within objects, further distinctions can be made according to the identity criteria ascribed to them.’ For geographic information, static biological strata have less influence, and mereological and physical strata not only have effects on internal semantic features but also function over the entire semantic structure. We can extract the following categories of semantic features:

Fig. 3.1
figure 1

Ontological strata (Guarino 1997)

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  • Matter (mereological): water, soil, clay, stone, sand, vegetable, artificial material, etc.

  • Appearance (morphological): flowing, standing, naturally curved, regular appearance, dimensionality, etc.

  • Size (morphological): large, medium, small, etc.

  • Function (functional): transportation, obstruction, inhabitancy, cumulating, tourism, breeding, etc.

  • Social class (social): political, economic, cultural, etc.

As an example, we can decompose the following into semantic geographic information features .

  • River—[water] + [flowing] + [naturally curved] + [transportation] + [linear];

  • Lake—[water] + [standing] + [tourism] + [breeding] + [area ];

  • Highway—[artificial material] + [transportation] + [constraint curved] + [linear] + [economic];

  • Fence—[artificial material] + [obstruction] + [regular] + [linear];

  • Building—[artificial material] + [inhabitancy] + [regular appearance] + [area ] + [obstruction] + [political and economic meaning ];

Of course, using only the identifying criteria of everyday world objects for geographic entities and phenomena has limitations. For geographic concepts such as a bay, a cape, or political boundaries (Smith and Mark 1998), we still extract their semantic features from a syntactic framework.

Structural Analysis of Semantics in Geographic Information

Structural semantics adopts implicational-lexical relations. Its main argument is that some words are implicitly associated with others in a language system ; therefore, the concept is an intrinsic language issue. The meaning of a word is dependent on its position in the lexical system .

According to this argument, semantic relations fall into four categories , i.e. synonymy, hyponymy, meronymy and antonymy (Buitelaar 2001).

Synonymy

Synonymy refers to words with the same or similar meanings . When representing geographic information, we use a strictly artificial language system . The represented objects are first classified, and then, the lexical system is prescribed upon the represented objects; thus, strict synonymy does not exist in such systems . However, if we look more closely at the potential lexical system of geographic information (both analogue and digital), similar semantics with multiple representations are quite common. It includes the following:

  • Multiple expressions of the same entity: variations of shape, colour and weight result in multiple expressions of the same entity.

  • Multiple expression of the same spatial relation : for example, the different expressions for a highway intersection (Fig. 3.2).

    Fig. 3.2
    figure 2

    Synonymy of the same spatial relation

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Hyponymy

Hyponymy also refers to a similarity relationship but to the similarity of classes . It involves the inclusion of classes . For example, the class ‘vehicles’ include both motor vehicles and non-motor vehicles.

It can be said that the deep foundation for word hyponymy is the hierarchical structure of concepts. Geographic ontology itself is a hierarchical structure (Smith and Mark 1998); thus, hyponymy has a reason to be an important relation in the lexical relations of geographic information. In terms of expression of geographic concepts, phonetics , lexics and syntax have the effect of constraint. However, the actual number of categories for language units is much smaller than the number of geographic concepts; consequently, they do not have a one-to-one relation. The following situations are possible:

  • A geographic concept has no related word; for example, fire does not appear on most map symbol systems ;

  • One geographic concept has one related word, e.g. chimney, cave, etc.;

  • One geographic concept has multiple related words, e.g. rivers can be denoted by single lines, double lines, etc.;

  • One geographic concept is a combination of multiple words; e.g. slope and valley;

  • Multiple geographical concepts are included in one word; for example, stadium includes the concepts raceway, stand, exit, etc.

  • Multiple geographical concepts correspond to one word; e.g. pond and lake have only one corresponding word.

These differences are the essence of representation: an infinite number of concepts can be expressed by a finite number of symbols.

Meronymy

Meronymy refers to the part–whole relation of objects or object classes as represented by words. In the linguistic structure of geographic information, meronymy is especially important for any geographic feature and it is essentially compound, consisting of many parts. Smith and Mark (1998) regard mereology as one of three basic tools for ontological investigations of geographic types, and mereology is actually the main concern of formal ontology in knowledge engineering (Simons 1987; Guarino 1995).

We can find meronymy in a geographic lexic system as follows:

  • Some words are composed of many parts by themselves. For instance, a block is actually composed of buildings, streets, squares, grass and so on, and a reservoir is composed of water bodies, boundaries, dams, etc.

  • Some words can be defined only in context . For instance, an exit must be defined as a part of a construction , a water boundary must be defined as a part of hydrological features , and so on.

While hyponymy has epistemic attributes, meronymy has strong ontological attributes. Meronymy is more dominated by the internal physical rules of reality .

Antonymy

Antonymy refers to the contrary relations of objects. There are different categories of antonymy, such as gradable antonyms, binary antonyms and relational antonyms. Antonymy is also reflected in geographic information as follows:

  • Morphology -driven antonymy—curve/straight, regular/irregular

  • Class -driven antonymy—Block/street, sea/land, mountain/plain, valley/ridge, urban/countryside

  • Attribute-driven antonymy—Highway/street, long-standing river/seasonal river

  • Relation-driven antonymy—above/below, overlaps/overlapped, contains/contained.

Spatial Syntax

Syntax is an important concept from linguistic systems viewpoints such as ‘phonetics -lexics-syntax’, ‘phonetics-syntax-semantics’ or ‘syntax-semantics-pragmatics ’, where syntax lies at the heart of the system . The function of syntax is to integrate language units with different physical features and conceptual meanings into higher language units that conform to rules and convey certain meanings .

Similar to phonetic and semantic structures, syntax also has an internal structure. In syntax (grammar), lexis and syntax are the two different units used to build words and sentences, respectively.

Elementary Spatial Relations in Geographic Information

The earth’s surface is an infinitely complex system . The linguistic paradigm regards geographic information as a hierarchical structure constructed by multiple levels of language units associated with various combination relations. As in natural language , revealing the internal structure of geographic information must start from the most elementary combination relations.

The types of spatial relations that exist between spatial entities is always a hot topic in GIScience (Egenhofer 1989). The following binary relations that reveal some combination relations from various angles.

Topological Relation

Topological relations refer to those relations that remain unchanged under topological transformations such as shifting, rotating and scaling, which were commonly used in early node-arc-polygon representations in digital maps (ESRI 1995).

The point -set based topological relation (Egenhofer and Franzosa 1991) greatly advanced scientific recognition of topological relations . The 4- and 9-intersection models mathematically, logically, and completely enumerate these topological relations . However, after it was discovered that they are somewhat less restricted in real-world situations, more metrical factors based on the idea ‘topology matters , metric refines’ were introduced to refine these relations (Egenhofer and Mark 1995; Shariff et al. 1998).

Topological relations are the most stable and yet most important relations in geographic features ; fortunately, that they are easy to cognize and store in computation systems . However, more combination relationships of different types must be investigated based on the following reasons.

  • First, topological relations are loose relations whose requirements are easy to meet. To further refine the spatial relations , we must seek other types of relationships. In language , some words can be defined within their full context .

  • Second, disjoint relations occupy the bulk of spatial relations in the real world . Thus, we also need other types of relations to describe these disjoint entities.

  • Third, as highly formalized descriptions, topological relations need semantic and ontological constraints in pragmatic contexts .

Metric Relation

Although topological relations can be considered as having been thoroughly investigated, we have little knowledge about what are roughly called metric relations .

Metric and topological are not opposing concepts; they are two aspects of the same spatially distributed phenomena . Different forms of topological and metric relations hold between any two spatial entities, and both can be computed from their positions. Topological relations provide the qualitative aspect, while metric relations provide other aspects of quantity. The only way to describe metric relation is to approximate graphics as accurately as possible in analogue representations.

Direction relations and distance relations can be defined between any two points , lines or areas . Because metric relations are difficult to process qualitatively way (unlike topological relations ), metric relations are neglected in most geographic information research. Some more complicated definitions come from the qualitative definitions of the direction and distance relations and are intended to simulate human qualitative reasoning (Peuquet and Zhan 1987; Papadias and Sellis 1994).

Combinational Qualitative Definition of Metric Relation

In a spatial distribution, we instinctively feel that some spatial relations are stronger than others: it is easy to form new features from some features; for others, it is more difficult; and for some, it is impossible. Thus, spatial relations have a combinatory function from a linguistic viewpoint:

  1. (1)

    Spatial relations can act as verbs that combine words into spatial propositions. Consider the two propositions in Fig. 3.3: ‘The bridge crosses the river’ and ‘The village is to the east of the river’. Under no circumstances can these be combined into a new proposition.

    Fig. 3.3
    figure 3

    Spatial sentence and phrase

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  2. (2)

    Language units with the same or similar meaning (synonymy or hyponymy) can form new sentences and can also easily be replaced by new higher language units.

  3. (3)

    Combination can occur only between those language units with certain spatial relations .

  4. (4)

    When 2 and 3 meet, the phonetics begin to take effect . The physical feature of the language units constrained the combination. Then, phonetics attribute is so-called Morphology , or Gestalt attributes (Guarino 1997).

  5. (5)

    Combinations are also constrained by surrounding structures; for example, combining city blocks is constrained by the structure of the street network.

Here, we find that topology plays a less important role than does the building pattern, and metric relations are more obvious here. To create further definitions of the spatial combinations of geographic entities, we need to further refine our spatial information theories, starting with a qualitative definition of metric relation.

Some scholars have noted that topological relationships in geographic domains are not genuinely topological in a topological sense (Smith and Varzi 1997). In fact, the most common topological examples involve shifting, rotating and scaling. Map projections are also included, but most of the projections are below second-order transformations.

If we suppose the following:

  • First-order transformations are limited to shifting, rotating and scaling, and that

  • map projections are below second-order, and their spatial scale is relatively small, then, the two values.

Definition 1

\( R_{1} = \left\{ {\begin{array}{*{20}l} {{\text{d}}_{34} /{\text{d}}_{12,} \,{\text{while}}\,{\text{d}}_{12} \ge {\text{d}}_{34} } \hfill \\ {{\text{d}}_{12} /{\text{d}}_{34,} \,{\text{while}}\,{\text{d}}_{12} < {\text{d}}_{34} ;} \hfill \\ \end{array} } \right. \)

where d12 and d34 are distances between point 1 and point 2 and between point 3 and point 4, respectively, and

Definition 2

\( D_{{\mathbf{a}}} = \left| {{\text{a}}_{12} - {\text{a}}_{34} } \right| \)

where a12 and a34 are the azimuth values between point 1 and point 2 and between point 3 and point 4, respectively, will remain basically unchanged. We can define an intermediate geometry, called combinational qualitative geometry (CQG), based on these two invariants, the length ratio and the difference in azimuth. From these two atomic properties , more qualitative aspects of the metric relation can be deduced.

Distance Combinational Relation

The distance syntagmatic relation is based on the invariant Rl. Suppose we have two line segments o1 and o2. We can distinguish the following two relations:

Definition 3

if Rl = 1, o1 and o2 are said to have an equal-length relation, notated as o1 El o2.

Definition 4

if Rl = 1/2, o1 and o2 are said to have a double-length relation, notated as o1 Dl o2.

The equal-length relation is a very common combinational relation in geographic space. Its ontological basis is that most spatial features —especially artificial features—have a statistically invariant magnitude range, such as the width of a street or the length of a river branch. In spatial associations, the occurrences of equal-length relations will increase dramatically.

Direction Combinational Relation

The direction combinational relation is based on Da. We can distinguish the following two relations:

Definition 5

Da = 0°. In this case, o1 and o2 are said to have a parallel relation, notated as o1 Pa o2.

Definition 6

Da = 90°. In this case, o1 and o2 are said to have a perpendicularity relation, notated as o1 Pp o2.

Parallel and perpendicularity relations are also very common relationships in geographic space. Their ontological basis is that the direction relation belongs to a circular measurement level , which has a much smaller variance range than does length. Second, the human ability to discern tiny angular differences is limited. Third, inherent physical rules result in more parallel and perpendicular distributive patterns in geographic space. Fourth, gestalt rules also influence artificial constructive features .

Composition of Combinational Qualitative Relations (CQRs)

The composition of CQRs with other spatial information results in a dramatic increase in the number of spatial relations . Generally, suppose we have two objects o1 and o2 that meet relations R and S, respectively. Their sum is denoted as R + S, thus

$$ {\text{o}}_{1} \left( {\varvec{R} + \varvec{S}} \right){\text{o}}_{2} \equiv {\text{o}}_{1} \varvec{R}o_{2} \vee {\text{o}}_{1} \varvec{S}{\text{o}}_{2} \,\,({\text{where}}\,\, \vee \,\,{\text{means }}\,\,{``}{\text{or}}{''}) $$

in atomic relations will result in a 2n sum of relations. Among these, the products of R and S are defined as follows:

$$ {\text{o}}_{1} \left( {\varvec{R} \circ \varvec{S}} \right){\text{o}}_{2} \equiv {\text{o}}_{1} \varvec{R}{\text{o}}_{2} \wedge {\text{o}}_{1} \varvec{S}{\text{o}}_{2} \,\,{\text{where}}\, \vee \,{\text{is }}\,\,{``}{\text{and}}{''} $$

Simple Composition of CQRs with Topological Relation Ml.

Noting those topological relations in which two linear features with intersected boundaries but null-intersected interior are present as Ml, we can define a simple composition as shown in Fig. 3.4,

Fig. 3.4
figure 4

Composition of CQRs with topological relation

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Pa ◦ Ml-Based Multiple Composition.

With Pa ◦ Ml-based multiple composition, we can define colinearity, sequence and direct neighbourhood relations.

Definition 7

For a set of line segments S = {o1, o2, …, on | n ≥ 3} if at least one oj ∈ S results in an oi (Pa ◦ Ml)oj for each oi ∈ S. Here, S is called a line colinearity set. Any number of elements above two have a line colinearity relation, notated as Cl.

Definition 8

For a set of points P = {p1, p2, …, pn | n ≥ 3}, if the set S = {li,j | 1 ≤ i < n, 1≤ j < n} composed of the connection of any two elements of set P is a line colinearity set, then P is called a point colinearity set. Any number of elements above two have a point colinearity relation, denoted as Cp.

Definition 9

For any sequence so = {oj | oj ∈ S} that is a subset of a colinearity set S, if oj(Pa ◦ Ml)oj+1 and Xoj Xoj+1 (where means ‘>‘ or ‘<‘) hold for each element oj and its successive element oj+1, so is called a sequence relation based on set S and notated as Sp. In contrast, Nd = {(oj, oj+1)} is a direct neighbourhood relation.

CQRs based on metric relations can be regarded as the atomic spatial relations of extended geographic features . They are immediately applicable to artificial and natural features such as block and pipe systems but may vary with when applied to most natural features with real geographic configurations. CQRs are to further lose their constraints.

Linguistic Anamorphosis of Spatial Relations

By defining CQRs, the deficiencies resulting from the too-loose constraints of topological relation and the too-strong constraints of metric relation can be overcome to some extent. CQRs can act as a combinatory mechanism between different levels of language units, acting in concert with topological and metric relationships to form a complete language structure.

Thus far, most GISs have depended heavily on Euclidean geometry. However, much research has revealed that the structure of geographic information is not merely a geometric matter ; instead, it is an ontological, epistemic and (natural) linguistic matter. Spatial relations provide us with syntactic rules that can establish linguistic structures that convey real and meaningful information only when integrated with phonetics and semantics.

Phonetic Anamorphosis of Spatial Relations

Compared with natural language systems , one of the particularities of geographic information as a linguistic system is that spatial relations as syntax is strongly related to the physical properties of their associated objects as phonetics , where scale and distance both play important roles.

The representation of spatial relations begins at the phonetic stage. As shown in Fig. 3.5, most spatial relations are presented by the usage of phonetic units.

Fig. 3.5
figure 5

Spatial relation by phonetics

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At the suprasegment stage, based on curves and minimal simple polygons , we can define more spatial relationships that are the phonetic anamorphoses of both topographic relations and CQRs, such as the sequences of the same level of curves, containing different levels of curves and contacting multiple levels of minimal simple polygons as in a double-line river system . In particular, CQRs lose their phonetic constraints to accommodate natural distribution situations, where curve-based parallel, perpendicularity relations and equal-length relations can be defined.

Syntactic Anamorphosis of Spatial Relations

In syntax, a spatial relation has two functional aspects. Based on the context in which it occurs, spatial relations can be grouped into two linguistic units, one is verbs and the other is constrained between language units. As a sentence, geographic information conveys ‘what is where’, and involves the following sentence types:

  • The building is there

  • The building is beside the river

  • The building is to the north of that building.

In a sentence of type 1, the words are implicitly connected with a reference system that reflects a spatial situation. A sentence of type 2 gives the spatial relation between two objects with different semantics; here, the relative positions of the objects are more important than their absolute positions. A sentence of type 3 gives the spatial relation between two objects with the same semantics. Although they are different points , the objects in this sentence are liable to merge into a new language unit when some neighbourhood condition is satisfied. In this case, the spatial relation tends to be constrained between the language units rather than acting as a verb.

Semantic Anamorphosis of Spatial Relations

From a geometric viewpoint , spatial information has various geometric components. One combination of the components can define only one spatial relation . As in the 9-intersection model, CQRs spatial relations stem more from the perspective of this type of geometric component analysis.

However, the semantics of spatial information also have an ontological basis. Using linguistic approaches, we can investigate ontological semantics based on the participants in relations as follows:

  • Dimensionality property: A certain spatial relation requires dimensionality for its participants. As an example, a containing relation requires an area object that acts as the container;

  • Active/passive: Some spatial relations imply an active/passive relation. For example, lines may be more active than areas in line/area relations: for example, roads pass through parks.

  • Vertical relation: Although two-dimensional spatial relations are defined on a plane, the participants do not always exist on a plane. The following situations are possible:

    • On one plane: e.g. a road and an adjacent farm field ;

    • Above: e.g. a bridge and a river

    • Below: e.g. a tunnel and a mountain

    • Uncertain: e.g. highways at a crossroads.

  • Compatibility: Some spatial relations require the participants to be compatible; otherwise, they are impossible in reality . For example, conceptual objects such as political boundaries can share locations with rivers, while highways cannot.

  • Spatial constraint property : Some spatial relations imply spatial constraints and correlations, such as parallel relations.

  • Cause property: In spatial relations such as colinearity, equal-length implies artificial construction . Some patterns imply certain natural causes.

Understanding the semantic features of geographic information is a prerequisite for humans to better understand geographic space. These features are linguistic knowledge that stands apart from concrete geographic configurations. Table 3.1 provides an example of how certain spatial relationships obtain their semantic anamorphosis in an ontological context .

Table 3.1 Semantic anamorphosis of the same spatial relation in different contexts
Full size table

Conclusion

In this paper, even merely from a microcosmic and technological approach, it is clear that the linguistic paradigm of geographic information has at least four aspects of significance for the development of GIScience , i.e. its paradigm potential, its ontological concern, its methodological guidance and its qualitative approach .

As a paradigm , linguistic research will promote geographic information into an information category with the most cognition and communication functions ; thus, it is an excellent theoretical platform for professionals in the fields of cartography, GIS, cognitive science , linguistics , computer science and Artificial Intelligence, and many other domains , and can accommodate research on both macroscopic and microcosmic levels , and from both functional and formal aspects. As a form of methodological guidance, linguistic research will inherit linguistic approaches in their entirety that have been developing for more than a hundred years; these include addressing geographic information in an integrated way, from phonetic , semantic and syntactic aspects—and even further—from pragmatic aspects. The comparative, structural and formal methodology that prevails in linguistics helps to reveal the internal structure of geographic information and can further guide the generation and understanding of geographic information in a computing environment. The philosophical perspective and qualitative approaches have been particularly concerned with linguistics for a long time , and they are increasingly concerned with knowledge engineering and GIS studies in the context of integrating knowledge into computing systems to gain robust computational and reasoning abilities.

In the framework of the linguistic paradigm , we have conducted some technical studies on map symbol recognition (Du 1998) and the linguistic analysis of a multimedia electronic atlas (Du 2001). Further research will include investigations of how physical features and ontological knowledge can be integrated into spatial relations to enhance the automatic understanding of geographic information systems and to evaluate how they can benefit spatial data mining and knowledge discovery. Moreover, the possibility of an investigation of map semiotic systems that include spatial, temporal and cultural coverage with the aim of revealing the evolution of human spatial cognition is also in our sights.

Part of this chapter was read at the International Cartographic Association during the 21st International Cartographic Conference (Duban, August 2003).