3 Credit Hours

Introduction to the conceptual and formal apparatus of mathematical logic, to mathematical concepts underlying the process of logical formalization, and to the applications of various logics across a broad spectrum of problems in computer science and artificial intelligence.

Prerequisites

Students should have some facility with basic concepts of propositional logic, set theory, and discrete mathematics (e.g., CSC 226 or LOG 335 or LOG 435), elements of the theory of computation (e.g., CSC 333), methods for constructing mathematical proofs, and some familiarity with the main ideas of software and hardware systems.

Course Objectives

• List and explain the principal types of logical languages;
• List and explain the principal applications of logics in a range of computing fields;
• Characterize and compare the expressive, computational, and practical properties of the principal logical languages;
• Evaluate the suitability of different logics to applications and choose logics appropriate to different tasks;
• Construct syntactically correct, well-structured logical theories;
• Translate between logics and other representations of information;
• Apply formal proof techniques to prove statements in logical languages or to construct counterexamples;
• Apply automated inference systems to formal logical representations;
• Explain and apply basic concepts for assessing and critiquing logical theories;
• Develop precise logical expression of intuitive ideas about computation and computational domains by applying logical languages and theoretical criteria to analyzing tentative formalizations of the ideas.

Course Outline

This course aims to introduce students to the conceptual and formal apparatus of mathematical logic, to mathematical concepts underlying the process of logical formalization, to methods of automated inference, and to applications of various logics across a spectrum of computer science problems.

Course Requirements

one final exam, seven homework assignments, a semester-long project, and weekly unannounced quizzes.

Textbook

(1) Introduction to Logic: third Edition by Michael Genesereth, Eric J. Kao.Genesereth, Michael, author Cham : Springer Nature Switzerland : Imprint: Springer, 2017. 3rd ed. Book Online at NCSU Libraries.
(2) Logic in computer science: modelling and reasoning about systems. Michael Huth, Mark Ryan. Huth, Michael, 1962- Cambridge [U.K.] ; New York : Cambridge University Press, 2004. 2nd ed. Book Online at NCSU Libraries.

Software Requirements

Familiarity with LaTeX or other systems for typesetting mathematical material can prove helpful, but is not required. Familiarity with logical and functional programming languages (Prolog, Lisp, Scheme) or the concepts of category theory can also prove helpful, but is not required.

Created: 04/16/2025