TR013: Knowledge Representation with Logic

Symbolic logic is a representational formalism for expressing knowledge and reasoning about such knowledge, in much the same way as calculus is used to represent and manipulate mathematical relationships in various disciplines of science and engineering. In this report we discuss two logical languages, namely, propositional calculus and predicate calculus, along with a brief introduction to the field of logic programming. A structural engineering example is described in detail to illustrate the concepts discussed in the report. Our emphasis is not so much on mathematical rigor as on conveying informally the essence of how logic can be usefully employed for creating knowledge systems in engineering domains. Thus we do not strive for completeness or mathematical precision; however, references to the appropriate material are provided throughout the report for the inquisitive reader.

This report is divided into four major sections. First, we discuss the syntactical (pertaining to the organization of symbols) and semantical (pertaining to the meaning of the symbols) aspects of propositional and predicate calculus in detail and provide a broad overview of a few tools for logic programming. The next section illustrates a prototypical application of logic for structural analysis. A representative implementation of such an application is the subject of Section 3. The final section presents some concluding remarks and suggestions for further reading.