# Course: Logic in AI

We are happy to announce that we will have a newly-designed course Logic in AI (course number: 0413153001) in the autumn and winter semesters of 2020. We will invite professors with different expertise coming from different countries to give us several lectures. Students who select this course not only can attend the lectures, but also can work on their interested research topics with the professor they choose. We also welcome people from other departments/faculties to listen to the lectures. The aim of the course is to enrich the knowledge we can provide from the course and enable more academic collaboration between China and other countries even during pandemic. Please find the information for the course below. After selecting the course, you can scan the QR code to join the group.

**Part 1: Deontic Logic**

Lecturer: Prof. John-Jules Meyer (Utrecht University in the Netherlands)

Abstract:

Deontic logic is the logic of obligations, prohibitions and permissions. More conceptually, it is the logic of ideal states of affair versus actual states of affair. As such it is a foundation of the fields of law and ethics, but also of normative systems and normative multi-agent systems, where agents are susceptible to norms while acting. In this course we will see how deontic logic can be viewed as a branch of modal logic. In order to deal with problems of proper representation, such as the infamous paradoxes of deontic logic, researchers have looked for alternative formalisations such as dyadic deontic logic and non-normal modal logic. In this course based on the book mentioned below, we will also look at a very abstract and general way of treating deontic logic, viz. input-output logic as proposed by Makinson and Van der Torre.

Textbook(s):

– Xavier Parent & Leendert van der Torre, Introduction to Deontic Logic and Normative Systems, College Publications, UK, 2018. ISBN 978-1-84890-269-5

**Part 2: Universal Logical Reasoning**

Lecturer: Prof. Christoph Benzmüller (Freie Universität Berlin in Germany)

Abstract:

Knowledge representation and reasoning applications in computer science, AI, philosophy and math typically employ very different logic formalisms. Instead of a \single logic that serves it all” (as envisioned already by Leibniz) an entire \logic zoo” has been developed, in particular, during the last century. Logics in this zoo, e.g., include modal logics, conditional logics, deontic logics, multi-valued logics, temporal logics, dynamic logics, hybrid logics, etc. In this lecture course I will introduce, discuss and demonstrate a recent attempt at a meta logical approach to universal logical reasoning that addresses this logical pluralism. The core message is this: While it might not be possible to come up with a universal object logic as envisioned by Leibniz, it might in fact be possible to have a universal meta logic in which we can semantically model, analyze and apply various species from the logic zoo. I will argue and demonstrate that classical higher order logic (HOL) [3] is particularly suited to serve as such a universal meta logic, and that existing reasoning tools for HOL can fruitfully be reused and applied in this context.

The lecture course will introduce HOL and the SSE technique, provide some hands-on introduction to Isabelle/HOL, study and demonstrate some concrete semantical embeddings of non-classical in HOL, and conduct practical exercises regarding the application of the SSE technique in philosophy, mathematics and artificial intelligence, including, normative reasoning and machine ethics. As far as time permits, the course will also explain and train the application of the LogiKEy methodology for designing normative theories of ethical and legal reasoning.

Check this site for preparation:

https://github.com/cbenzmueller/LogiKEy/tree/master/CoursesAndTutorials/2020-ZhejiangUniversity

**Part 3: Logic and Philosophy of Computation for AI**

Lecturer: Prof. R. Ramanujam (The Institute of Mathematical Sciences in India)

Abstract:

The question, “What is an algorithm?”, has important philosophical dimensions: ontological, methodological and ethical. Mathematicians and physicists are used to talking of “in principle” solutions, leaving it to implementations to work out the details. But what if there is another principle that limits implementations as well? Complexity and resource consciousness are modern concerns, both in the physical world and in the world of ideas.

In the last 70 years, computer science has not only given us an amazing tool that has transformed the world but also connected it up in ways unimagined before, demonstrating flexibility unparalleled in history. This course aims to study basic philosophical questions relating to theory of computation.

The first half of the course is a discussion of questions like: What is an algorithm? What is a computer? What is a computer program? What is complexity? What is physical computation? Can computation involve randomness?

The second half of the course revisits these philosophical concepts in the context of Logic and AI, examining how notions like the nature of time, knowledge, communication, agency etc are relevant in the context of computing agents, and can be studied using formal logics.

Textbook(s):

- Philosophy of computer science, by William J Rapaport, SUNY Buffalo, USA, April 2020.
- Papers will be assigned for reading.
- Questions: curtainraiser

**Part 4: Argumentation**

Lecturer: Prof. Beishui Liao (Zhejiang University in China)

Abstract:

In this section, we will introduce theories and approaches for the reasoning under the context of disagreement, including traditional nonmonotonic logics and computational argumentation. More specifically, we will first introduce default logic, logic programming and their recent developments, and then abstract argumentation, structured argumentation, and their application to some emerging areas, such as AI ethics and legal reasoning.

Textbook(s):

- Beishui Liao. Efficient Computation of Argumentation Semantics, 1st Edition, Academic Press, 2014, ISBN: 9780124104068
- Pietro Baroni (Editor), Dov Gabbay (Editor), Massimilino Giacomin (Editor). Handbook of Formal Argumentation, College Publications, 2018, ISBN: 978-1848902756