Spatial Knowledge Representation and Inference

Geographical knowledge may be structured or unstructured. We may organize our knowledge in a highly structured form so that problems can be solved by sys tematic and rigid procedures. Mathematical models, statistical methods, and heuristic procedures are knowledge in procedural form. They follow a rigid framework for the representation and analysis of structures and processes in space and time. Procedural knowledge is effective in system specification, calibration, analysis, scenario generation, and forecasting of well specified and structured problems. Through research, we have accumulated, over the years, a wealth of procedural knowledge which can be effectively utilized for geographical analysis in spatial information systems.

A majority of our knowledge, however, is loosely structured. Subjective experience, valuation, intuition, and loosely structured expertise often cannot be appropriately captured by rigid procedures. They are declarative in nature and can only be represented by more flexible frameworks. Making inference on such knowledge structures cannot follow strict procedures championed by procedural knowledge. Problem solving by if–then arguments is a typical example of using declarative knowledge for decision making. This type of knowledge is effective in solving unstructured or semistructured problems. It is suitable for inference with concepts, ideas, and values. Similar to the use of procedural knowledge, declarative knowledge can be utilized in spatial decision making, especially with spatial information systems. Declarative knowledge is, however, ineffective to solve highly structured problems. Consequently, procedural and declarative knowledge have to be used in synchrony throughout a decision making process.

Once a spatial structure or process is understood and can be specified in a formal and structured manner, we can always capture it by a mathematical model or procedure. The representation of loosely structured knowledge is, nevertheless, not as straightforward. Declarative knowledge representation and inference have thus become a main concern in building spatial reasoning systems with artificial intelligence. To be able to understand and to reason, an intelligent machine needs prior knowledge about the problem domain. To understand sentences used to describe geographical phenomena, for example, natural language understanding systems have to be equipped with prior knowledge about topics of those phenomena. To be able to see and interpret scenes, spatial vision systems need to have, in store, prior information about objects to be seen. Therefore, any intelligent system should possess a knowledge base containing facts and concepts related to a problem domain and their relationships. There should also be an inference mechanism which can process symbols in the knowledge base and derive implicit knowledge from explicitly expressed knowledge.

Knowledge representation formalism consists of a structure to express domain knowledge, a knowledge representation language, and an inference mechanism. Conventionally, its duty is to select an appropriate symbolic structure to represent knowledge in the most explicit and formal manner, and an appropriate mechanism for reasoning.

Through evolution and civilization, human beings have developed a sophisticated way, namely our natural language systems, of representing knowledge. We are able to name and to describe facts by natural language sentences, and are able to reason and to infer with facts and beliefs. This mechanism of representing facts and inferring with knowledge may be captured by logic. Though logic is not a theory on knowledge representation, it provides formalism for reasoning about beliefs. It consists of a syntax, a semantic, and a proof theory which can be utilized for knowledge representation and inference. Propositional logic and predicate logic are typical paradigms.

However, human knowledge is usually imprecise and our inference often consists of a certain level of uncertainty. While uncertainty is of various sources, the one that stems from imprecision is rampant in human systems. To represent and infer with such knowledge, we need a logical system which can handle imprecision. Among existing paradigms, fuzzy logic appears to be instrumental in processing imprecision. Fuzzy logic is a nonstandard logic for approximate reasoning. It is a formalism for drawing possibly imprecise conclusions from a set of imprecise premises. A premise is fuzzy if it has imprecise predicates. In the narrow sense, fuzzy logic is a formalism of approximate reasoning. In the broad sense, fuzzy logic is the theory of fuzzy sets.

Though first order predicate logic gives a powerful mathematical tool to represent knowledge, its theorem proving mechanism is not too efficient and flexible to handle spatial reasoning consisting of a large decision tree or a long chain of inference involving a large set of if–then statements. A system containing an ordered set of if–then rules is called a production system. It can be employed to perform tasks involving deep knowledge reasoning.

Unlike logic and production rules which store knowledge independent of each other and with no interconnections between them, a semantic network is a highly interconnected hierarchical representation of knowledge consisting of a set of nodes connected to each other by a set of directed labeled links. Mathematically speaking, it is a labeled, directed graph. The nodes represent objects which can be facts, events, situations, actions, concepts, sets, individuals, propositions, predicates, terms, descriptions, and procedures. The links represent relationships between the objects. A semantic network provides a structure with which knowledge can be formally represented and efficiently retrieved. Retrieval and inference thus become a search for paths between nodes or a match of patterns in the network. Though semantic networks were developed for the purpose of representing the English language, it turns out to be a rather pictorial and effective tool for representing binary spatial relationships and perhaps human associative memories.

Similar to semantic networks, frames are hierarchical representations of knowledge. They in a way can be interpreted as complex semantic networks with internal structures. Frames are generally used to represent prototypical knowledge or knowledge with well known characteristics. Differing from logic and production rules which store knowledge in small independent trunks, frames store knowledge in larger interconnected chunks (conceptual entities). A knowledge base is then a collection of frames.

A weakness common to semantic networks and frames is that knowledge representation lacks a well defined structure. Knowledge abstraction, encapsulation, and modularity which are considered as salient features of knowledge representation are not effectively realized in semantic networks and frames. These characteristics however can be captured by the object oriented approach. Under the object oriented framework, the real world is represented as a hierarchical set of objects linked by some protocols of communication among them. An object is an independent entity consisting of its own attributes (variables) and methods (operations, procedures, actions) that work on them. The attributes depict the state of an object and the methods are used for intraobject controls and inter object communications. The object oriented approach possesses the advantages of knowledge encapsulation and inheritance. It can make spatial knowledge compact and facilitate inference.

In addition to the major formalisms discussed above, other paradigms such as conceptual dependency, script, CYC, logical programming, and case based reasoning are also potentially useful frameworks for spatial knowledge representation and inference. Though each of the formalisms has its unique structure, they are in some ways related and can be made complementary to each other. It is possible to develop hybrid knowledge representation languages which can take advantages of the salient features of individual languages.