P251 | 9738 | Weiner

This course is designed to delve deeper into issues that were broached in p250. As in p250, our central concern is with the (semantic) notion of the validity of an argument and with techniques (both semantic and syntactic) for determining whether or not arguments are valid. In this sequel to p250, we will look at more sophisticated formal languages. We will begin with a quantificational language in which we can express complex statements involving two place predicates (e.g., ‘x loves y’), three place predicates (e.g., ‘x is between y and z’), etc. We will study symbolization, formal logical theories (including a tableau method as well as a natural deduction method for establishing the validity of an argument) and model theoretic interpretation. We will then proceed to introduce more expressive power into our formal language and formal theories by the addition of techniques to express functions (e.g., the successor of x, the mother of x), and identity. Time permitting, we will also do a bit of modal logic, multi-valued logic and/or set theory. There will be weekly homework assignments, two mid-term examinations and a final examination. P250 is the prerequisite for this course.