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From Predicate Modeling to Semantic Analysis of Predicates: the Use of Logic in Computer Science

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From Predicate Modeling to Semantic Analysis of Predicates: the Use of Logic in Computer Science From Predicate Modeling to Semantic Analysis of Predicates: The Use of Logic in Computer Science Ken Archer Chief Technology Officer Telogical Systems 6756 Old McLean Village Drive, McLean, VA 22101, USA Email: {karcher}@telogical.com Abstract: Since the introduction of independent data storage order logic (FOL) as a purely formal system in computer mechanisms in the 1970s, database design has been science by revisiting the history of FOL. The absence of a characterized by the modeling of predicates, or attributes, and principle controlling when new predicates should no longer their interrelationships. This paper critiques prevailing data be created is fundamentally rooted in FOL as the theoretical modeling methodologies – relational data modeling and AI- basis of these information modeling techniques, as FOL also based fact modeling in RDF and OWL – as leading to the lacks such a principle of restraint. This paper suggests that, unrestrained creation of predicates in information models. based on the history of FOL, the more appropriate use of The absence of a principle controlling when new predicates FOL is as a grammar for expressing the results of semantic should no longer be created is fundamentally rooted in the analysis. It is claimed that the purpose of FOL was never to theoretical basis of these information modeling techniques – express any and all predicates that could ever been spoken or first order logic (FOL) – which also lacks such a principle of written, but to express the predicates emerging from semantic restraint. The paper then proceeds to revisit the larger logical analysis as relational, functional predicates. Semantic project within which FOL emerged, semantic analysis, which analysis thus constitutes the overarching logic program of does guide the selection of appropriate predicates. It is which FOL is merely a part. If computer science and claimed that the purpose of FOL was never to express any artificial intelligence seek fidelity to logic, it is claimed here, and all predicates that could ever been spoken or written. then semantic analysis must become a central discipline and Rather, FOL provides a grammar suitable for expressing the critical first step in computation. The paper reviews results of semantic analysis. If computer science and approaches to semantic analysis and makes recommendations artificial intelligence seek fidelity to logic, it is claimed here, for the future of semantic analysis. Finally, a thorough then semantic analysis must become a central discipline and history of the concerns of modern logic that led to semantic critical first step in computation. The paper reviews analysis and FOL is provided, with a concluding revision of approaches to semantic analysis and makes recommendations the common misconception that the formality of FOL implies for the future of semantic analysis. Finally, a thorough lack of intentionality or semantics in FOL. history of the concerns of modern logic that led to semantic analysis and FOL is provided, with a concluding revision of 2. The Uncontrolled Role of Predicates in the common misconception that the formality of FOL implies Computer Science lack of intentionality or semantics in FOL. Keywords: logic, first order logic, predicate logic, semantic Overview of Uncontrolled Predicate Identification analysis, relational databases, databases, relational algebra, events, event ontology, ontology, business rules, complex Predicate-based facts have always played a special, central event processing, event processing, RIF, RDF, OWL. role in artificial intelligence and computer science more generally as the conceptual unit constituting a computer’s 1. Introduction state. Any system for automated reasoning requires a corresponding representation of the world about which a Declarative software architectures are anchored in a system is to reason, and the traditional foundation of logical model of a domain. In particular, states of a domain representation of knowledge of the world is a foundation of are modeled as a collection of fact types, which provide facts made up of predicates. The oft-cited knowledge semantic details to an otherwise formal system of functional representation hypothesis of Brian Smith asserts that any predicates rooted in first order logic. This model of fact “mechanically embodied intelligent process will be types then constrains a set of stateful facts that describe comprised of structural ingredients that we as external isolated states of the domain and physically persist in a data observers naturally take to represent a propositional account store whose design – from relational databases to triple stores of the knowledge that the overall process exhibits”. [2, my – is based on the same formal system from first order logic. italics] The assumption that reality consists of a set of This paper questions this predominant manner of using first atomic facts is so central to artificial intelligence that it is one of the targets of Dreyfus’ critique of AI (Dreyfus calls it the “ontological assumption”). [1] FOL simply provides a grammar for the relational treatment of predicates, and does not itself include any The primary role played by predicate-based facts in principle that would restrain which predicates should be intelligent systems has been formulated in very influential expressed in a FOL-based model of a domain. This is terms by the business rules consulting community, the because FOL is not itself a modeling methodology, but is leaders of which formed the Business Rules Manifesto: itself merely a tool of modeling methodologies that were “Terms express business concepts; facts make assertions formulated and developed prior to and during the about these concepts; rules constrain and support these development of FOL. These previous methodologies, known facts.” [4] as analysis or semantic analysis, are the topic of the next section. What is demonstrated here is that the modeling This section argues that predicates, while obviously methodologies used in computer science drew on FOL, but critical to the definition of an information model, are not on the broader semantic analysis methodologies that had currently uncontrolled in their assignment to particular provided the overarching purpose and use for FOL. models. That is, methods for information modeling – e.g. relational data modeling and OWL modeling – are essentially FOL-Based Information Modeling methods for attribute identification that themselves do not clearly prescribe when attributes should not be added to a The specific influence of FOL on information models has model, and should instead be defined in logical terms based been felt in two important areas: relational data models and on existing attributes (e.g. as business rules). This lack of a Semantic Web standards such as RDF. The result of this principle of limitation on the attributes included in an influence is that both information modeling techniques information model is rooted in a similar lack of such a provide formal structure that was missing in previous principle in first order logic, which provides the theoretical approaches to data modeling, a structure based on the foundation for these modeling methods. It is to first order functional approach to predication taken by FOL. logic that we thus now turn. Relational data models emerged in a time when data was First Order Logic stored in files tightly integrated with particular applications. Because there was no possibility of sharing application- Facts express atomic states of the world via tuples specific data with other applications, the structure of such consisting of a subject and a predicate. A predicate, in turn, files was not designed independently of the application. A consists of an object and a value, as is demonstrated in the common element of such databases – found in both example below. hierarchic and network databases – was that relations (e.g. employment, parenthood) were stored in links between tables Fact: The sky is blue. while tables stored information about entities. While this Subject = the sky enabled fast performance of data retrieval operations, the Predicate = is blue encoding of relations in links between tables prevented tables Object = has a color from entering into different relations to meet the needs of Value = blue other applications. The primacy that facts have in knowledge representation In 1969, Codd turned to FOL to provide a formal basis for owes in large part to the primacy facts have in first order a database model in which data could be stored in a logic (FOL). Facts are the atomic elements of FOL, whose declarative model, independent of the algorithmic needs of breakthrough was to take a functional approach to predicates particular applications. Rather than encoding relations in the of facts. Specifically, FOL treats predicates as functions that links between entity-based tables, Codd makes relations the map bare particular instances (x) to a predicate class of basis of the tables themselves by leveraging the unique instances (F(x)). This hard distinction between class terms ability of FOL facts to express all information as relations. and terms for bare particulars or naked instances is central to Instead of ‘employment’ being stored in the link between a FOL. For example, the fact “Acme Supply is a customer” is ‘company’ fact and a ‘person’ fact, ‘has employer’ is a denoted in predicate logic as C(x), where C=Customer and column of a ‘person’ table with employers as values, a the function maps to true when x=Acme Supply. structure based on the FOL expression of ‘has employer’ as a two-place predicate relating persons and employers. Each What is most significant about the functional approach to row of a table in the relational data model is a set of such predication in FOL is its use of relations as the basis of logic. relations, or, FOL facts. The table structure of Codd’s In contrast to Aristotelian logic’s grounding in entities that relational data model is thus based on FOL tuples, such that, have properties and may enter into relations with each other, in the words of Codd’s first rule of relational databases, “All FOL is based on relations themselves.
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