Mathematical Sciences for Artificial Intelligence

General objectives To provide the student with the fundamental formal notions of two basic aspects of the preparation of an artificial intelligence scientist, mathematical logic and probabilistic methods in computer science. The two sections of the course are dedicated to these two aspects. The first part of the course aims to introduce mathematical logic as a powerful tool for modeling and formally reasoning on different aspects of artificial intelligence, in particular data management, knowledge representation, querying and data review. and knowledge. The second part of the course aims to illustrate some fundamental aspects of the probabilistic methods in computer science such as the design and analysis of probabilistic algorithms, sampling and probabilistic allocation methods, stochastic processes and some of their applications to data analysis and machine learning. Specific goals Knowledge and understanding For to the first part of the course, the student learns the fundamental notions of mathematical logic, the principles according to which the validity of arguments is judged, the relationships between arguments are analyzed and inferential relationships are evaluated, such as deduction, induction and abduction, among them. Compared to the second part of the course, the student learns the basic notions of the design of probabilistic algorithms and their analysis and acquires the basics to apply these notions to the design of fundamental algorithms in Artificial Intelligence, including search and sorting algorithms, algorithms on networks and graphs, classification algorithms, clustering and machine learning. Apply knowledge and understanding The student gains a deep understanding of the role of logic in various aspects of artificial intelligence and basic knowledge to formalize a problem in logic, analyze logical theories and reason on related inferences, build logical theories for modeling knowledge bases of medium complexity, specify logic queries of databases and knowledge base and translate the specification of simple computations into logic programs. The student acquires a deep understanding of the role of probability in the design of algorithms and in data analysis and acquires basic knowledge to carry out analysis of probabilistic algorithms, define probabilistic algorithms for problems of medium complexity, apply fundamental methods such as Monte Carlo method, Markov chains, dynamic programming and Bayesian models in different contexts, such as sequences, graphs, networks, machine learning, classification and clustering. Critical and judgmental skills The student is able to evaluate the validity of statements and arguments, the coherence of a set of axioms in a knowledge base, the adequacy of the formulation of a computation that extracts data from a data and knowledge base, the correctness of a logic program with respect to the specification of certain properties. The student is able to analyze probabilistic algorithms, to evaluate the effectiveness of probabilistic and dynamic optimization methods for algorithmic and Artificial Intelligence problems and to judge the quality of the application of machine learning, classification and clustering algorithms. Communication skills The practical activities and exercises of the course allow the student to acquire crucial tools to communicate and share the critical evaluation of logical tools and languages and their role in artificial intelligence and algorithmic methods and their role in different important contexts of Artificial Intelligence. Learning ability In addition to the classic learning skills provided by the theoretical study of the basic topics covered in the course, the methods used for the course, in particular the programming activities, stimulate the student to autonomously study some topics, to work in groups and to develop concrete applications of the concepts and techniques learned during the course.