Unit 4: Logic, Inference and Ontology

Commentary

Knowledge representation, logic, and reasoning have been the core of artificial intelligence since it was founded at Dartmouth College in 1956. Although new approaches have been successfully introduced and explored in recent decades, such as connectionist, and evolutionary and probabilistic solutions (which will be introduced in the later units of this course), knowledge-based methods continue to emerge and play important roles in both theoretical and practical research projects and systems. An example of this is the emergence of semantic Web, which from an AI point of view, is a combination of Web- and knowledge-based technology in the Internet age.

This unit introduces the main aspects of the fundamental issues of AI relating to knowledge representation, logic, and inference. It also provides the basis for the remaining units of this course. The problem-solving approaches introduced in previous units, such as search and CSP, serve as the main techniques for solving the knowledge-based problems introduced in this unit.

Unit Purpose

When you complete this unit, you will be able to

• Discuss the syntax and semantics of both propositional and first-order logic.
• Explain the mechanisms of reasoning in propositional and first-order logic.
• Design and implement several main reasoning algorithms, such as resolution, theorem proving, and backward and forward chaining.
• Describe knowledge representation and reasoning for actions, situations, mental objects, and under default information.
• Explain ontology and description logics, and their reasoning techniques in both knowledge engineering and semantic Web context.

Section 1: Propositional logic and reasoning
Section 2: First-order logic: Syntax and semantics
Section 3: Inference in first-order logic
Section 4: Ontology and description logics
Section 5: Knowledge representation of actions, situations, and mental beliefs
Section 6: Reasoning with default information

Readings

Supplemental Unit Readings

Papers:

Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., and Tompits, H. (2008). Combining answer set programming with description logics for the Semantic Web. Artificial Intelligence, 172(12-13), 1495-1539.

Ohlbach, H. J., and Koehler, J. (1999). Modal logics, description logics and arithmetic reasoning. Artificial Intelligence, 109(1-2), 1-31.

Grant, J., Kraus, S., and Perlis, D. (2005). A logic-based model of intention formation and action for multi-agent subcontracting. Artificial Intelligence, 163(2), 163-201.

Books:

Enderton, H. B. (2001). A mathematical introduction to logic (2nd ed.). St. Louis, MO: Elsevier.

Brachman, R. J., and Levesque, H. J. (2004). Knowledge representation and reasoning. St. Louis, MO: Elsevier.

Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D., and Patel-Schneider, P. F. (2007). The description logic handbook: Theory, implementation and applications (2nd ed.). Cambridge, NJ: Cambridge University Press.

Activities

• Browse the books listed as Supplemental Unit Readings, and read any topics that pique your interest or will be useful to you for further research.
• Explore other research and application activities relating to logic and knowledge, such as high order logic, modal logic, advanced logic programming, semantic Web, large scale knowledge base, and ontology projects.
• Discuss your findings and your interpretation of the material in the course conference.