Formal logic for open minds

After completing this course students are able to:

1. Demonstrate knowledge of the key terms and concepts of logic, including propositional logic and first-order logic.
2. Demonstrate understanding of the difference between different logical languages and their expressive power (complexity), and the role soundness and completeness play.
3. Apply formal logical analysis to complex aspects of language and argumentation.
4. Practice natural deduction proofs.
5. Demonstrate understanding of the conceptual underpinnings logical systems and their applications in various fields,

Relation to assessments:
Participation (10%) goals 1-4
Project (20%) goal 5
Two written exams (35% each)  goals 1-4.
 

Much of our interaction with each other in daily life has to do with information processing and reasoning about knowledge and ignorance of the people around us. When we ask a simple question, we convey the information that we do not know the answer, and also, that our addressee may know it. Indeed, in order to pick out the right person for asking such informative questions, we need to reason about knowledge of others. It is our ability to reason in the presence of other reasoning agents that has made us historically so successful in debate, organization, and in planning collective activities. And it is reasoning in this broad sense that this course is about.
In this course, logic will be presented as a key element in the general study of reasoning, information flow and communication: topics with a wide theoretical and practical reach. The course starts with introductions to three important systems of reasoning: propositional logic, syllogistics, and predicate logic. Together, these describe situations consisting of objects with a great variety of structure, and in doing so, they cover many basic patterns that are used from natural language to the depths of mathematics. Next, we move on to the newer challenges on a general agenda of studying information flow. The first is agents having information and interacting through questions, answers, and other forms of communication. This social aspect is crucial if you think about how we use language, or how we behave in scientific investigation. We will model observation and reasoning in a multi-agent setting, introducing the logic of knowledge, and the use of games as a model of interaction.
The overarching goal of this course is to show the multiple facets of modern logic and its applications at the cross-roads of exact sciences, humanities and social sciences. Various logics are used to analyze knowledge and belief, justification and evidence, obligation and permission, necessity and possibility, time and temporality, action and causation, and much more. These phenomena play a central role in our understanding of how language, mind, information and even the world work, and as such are essential in many areas, including, but not limited to, linguistics, philosophy, law, cognitive science, and computation.


Format
the class will primarily consist of two types of sessions, those led primarily by the instructor (to cover new content) and labs led by the students (to practice and work on homework assignments), as well as student presentations in the final weeks of the class.