Course Description

• Introduction and Motivation. Reasoning about action and event is one of the most mature research areas in Artificial Intelligence (AI): it is almost as old as AI itself. This research area has a direct connection to one of the central AI topics - namely, how to solve a problem using general domain independent techniques for finding a sequence of transformations or constructors/destructors that create a desired partially specified goal from a given initial state of affairs. This research area has strong foundations in mathematical logic. It is influenced and inspired by modern research in logic, knowledge representation, natural language understanding, high-level robot control, database transactions, and several areas in computer science. The growth in this area was to a significant degree stimulated by research done in Toronto (in Canada), and in a few other universities world-wide. This area consists of several sub-areas, where researchers are seeking different ways to overcome computational difficulties associated with reasoning about effects of actions (events) in large, incompletely known application domains. The major areas of application are lifted planning (i.e., planning on the level of action schemas), problem solving, discovery in natural sciences, control of hybrid and embedded systems, computing causes of failures from traces (logs of events), high-level robot control, verification of business processes, database transactions, multi-agent systems and languages.

  This course starts with basic introduction to mathematical logic: prepositional logic and first order logic. The students are expected to learn a professional logical jargon and concepts that will help them to work on a higher level of abstraction. This logical language serves to provide a formal specification that facilitates a correct implementation in one of the programming languages. Moreover, using logical specification, it becomes possible to formulate interesting, general and realistic AI research problems that cannot be stated in other terms. After that, we review the most important results in this research area, and then focus on modern developments. We will discuss the compromises involved in providing useful logical representations that allow reasoning about actions to remain computationally tractable. There are some limits imposed by computational tractability; we will mention what we can do when trying to develop efficient AI implementations.

  The assignments will include problem solving exercises, but one of the assignments on planning may include also running a benchmark problem using the state-of-the-art planners and comparing several planning heuristics.

  Topics include: an algorithm for correct reasoning in propositional logic and in first order logic, the situation calculus, the projection problem (whether a given state can be reached after executing a given sequence of actions when initial states are not known completely), regression (reasoning backwards), progression (reasoning forward), the frame, and ramification problems, the precondition and successor state axioms, planning, execution monitoring, reasoning about effects of continuous and concurrent processes extended in time, identifying an actual cause of an observed effect from logs of events that happen during the run of a system.
  It was long time recognized that actions have not only direct, but also indirect effects, and in many cases, have no effect on most of the features characterizing application domains. For example, pressing an electric switch button has a direct effect on the button - it becomes pressed - but also has an indirect effect, e.g., lights turn on. It turns out that chains of mutual dependencies leading to indirect effects may be quite complicated. We may consider representations developed to specify non-effects succinctly and to reason about indirect effects correctly. For the latter purpose, representations based on causality turned out to be most successful. We may explore some of the recent results about using causality to compile implicit indirect effects into explicit effects.
  If time permits, the course may include several optional advanced topics including complex actions and procedures, their applications to cognitive robotics, stochastic actions and related computational problems.
  This course provides necessary and sufficient background for the students who would like to be involved in research on reasoning about actions in artificial intelligence.

• Prerequisites An undergraduate level course in AI (e.g., CPS721 at TMU) helps, but it is not required. An undergraduate level course on Discrete Mathematics is strongly recommended. The students are expected to have strong interest in logical (symbolic) AI, in particular, in Knowledge Representation and in Automated Planning. No previous knowledge of Machine Learning is required. This course has no relation to Machine Learning; instead, the focus is on correct logical reasoning. Since no previous knowledge of mathematical logic is expected, this course starts with a brief introduction into propositional logic, and first order logic. In addition, a popular reasoning algorithm based on semantic tableau is also introduced and illustrated on several examples.
  
• Delivery Mode: Lectures: 3 hours. Assigned readings, out-of-class discussions (in a tutorial or a lab) might be possible too.
  The course is delivered in-person including 3 (2+1) hours of lectures per week, for 12 weeks. All the presentation slides, except of problem solving sessions, will be posted on D2L to facilitate asynchronous learning.
• Calendar Description: The course will focus on the theory and implementation of discreet dynamical systems considered from the perspective of artificial intelligence. Modern logical representations of actions and their effects will be discussed in detail. The emphasis will be on the compromises required to ensure computational tractability of reasoning about effects of actions. The course will show how these research issues are relevant to artificial intelligence and to applications beyond the traditional area of artificial intelligence. Topics may include: logical foundations, reasoning about direct and indirect effects of actions, lifted planning, time and concurrency, causality, stochastic actions.
• References: 
  There is no mandatory textbook. Handouts with slides will be posted on D2L after every class.
  Recommended Textbooks (some of the readings are optional and/or supplementary to your lecture notes)
  • The book How to prove it : a structured approach by Daniel J. Velleman provides foundations and a very readable introduction to a few basic topics. It can also serve well as a reference. Published by Cambridge University Press in 2006, 2nd edition, ISBN 978-0521675995 (paper-back). Alternatively, consider Edward A. Bender, S. Gill Williamson ``Short Course in Discrete Mathematics", Dover, 2005. ($14 on Amazon.ca). See sections on Functions and Order posted online in PDF. Alternatively, recall differences between function and relation from a short and readable overview of The Language and Grammar of Mathematics, published as Section I.2 (Part 1 "Introduction"): pages 8-16, in Timothy Gowers (Editor) The Princeton Companion to Mathematics, Princeton University Press, 2008.
  • Uwe Schoning `` Logic for Computer Scientists", published by Birkhauser, Boston 2008 (Available online: see Ryerson Library.) A paperback edition is $33 on Amazon.com). [Skip resolution, since we consider only a semantic tableau algorithm for logical reasoning: Sections 1.1 - 1.2, and Sections 2.1 - 2.2].
  • Mordechai Ben-Ari ``Mathematical Logic For Computer Science'', corrected 6th printing of the 2nd edition, Springer 2003, or a more recent edition of this book. The recommended 3rd edition of his book was published in 2012. [This is a textbook for a Ryerson course MTH714. Concentrate on Section 2.6 , Section 5.5 and skip the rest].
  • Stephen Cook:   Slides for the course CSC 438S/2404S: Computability and Logic. The following slides can be relevant: Propositional Calculus, read pages 2-6 only, and Predicate Calculus, read the pages 18-26 only.
  • Elliot Mendelson ``Introduction to mathematical logic", any recent edition is fine.
  • Joseph R. Shoenfield ``Mathematical Logic" (paperback). Publisher: A K Peters/CRC Press, 2001. ($42 on Amazon.ca) [Chapters 2 and 3].
  • Ronald Brachman and Hector Levesque ``Knowledge Representation and Reasoning", published by Morgan Kaufmann, 2004. ISBN: 978-1-55860-932-7 [Chapters 14, 15.1 and 16]. Available in the university library.
  • Raymond Reiter `` Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems". MIT Press, 2001. [ Available online from the Ryerson library: Chapters 3, 4, 5, 7, 9, 10.]
  • Hector Geffner and Blai Bonet: A Concise Introduction to Models and Methods for Automated Planning, 141 pages. This book is available online from the Ryerson Library. This book was published in June 2013, by Morgan and Claypool publishers, in the series Synthesis Lectures on Artificial Intelligence and Machine Learning (doi:10.2200/S00513ED1V01Y201306AIM022).
  • S. Russell and P. Norvig "Artificial Intelligence", published by Pearson. The following chapters are relevant: Planning (Chapter 11) from the 2nd edition, 2003, p. 375-416, ISBN 0137903952; Solving Problems by Searching (Chapter 3), from the 3rd edition, 2010, p. 65-122, ISBN 0136042597.
  • Frank van Harmelen, Vladimir Lifschitz, Bruce Porter (Editors) " Handbook of Knowledge Representation", published by ELSEVIER, 2007, 1034 Pages, ISBN: 978-0-444-52211-5. [Chapters 3, 16, 23.] Available in the university library.
  • Optional/required readings may also include a selection of research papers published in journals or in the proceedings of international conferences.

• Student Evaluation See the table at the bottom. There are two exceptions. First, any student who missed half or more than half of the lectures fails the course for non-attendance. Class attendance is mandatory. Second, any student who did not submit 3 out of 5 homework assignments is deemed to fail this course. Home work includes mostly problem solving.
  The students have to complete a term project in addition to homework and do in-class presentation. The scope and requirements to the term project will be announced in the beginning of November. Project proposals must be uploaded to D2L before the deadline. The project must include original research on one of the topics related to the course. The final course project report must include the precise formulation of the problem, a detailed description of a proposed solution, and possibly formal proofs of the statements and/or a computer implementation. The possible presentation topics will be announced via D2L in October. The presentation includes preparing detailed slides and giving a talk for 40-50min in class.
• Lecture Topics (tentative list):
  1. Introduction to propositional logic. Syntax: well-formed formulas, sub-formulas of a formula, defined connectives. Semantics: truth assignment, satisfiability, tautology, logical consequence, well-known propositional equivalences. DNF (disjunctive normal form), CNF (conjunctive normal form), NNF (negation normal form). The satisfiability problem for a formula in propositional logic. The entailment problem. Reasoning in propositional logic using semantic tableau: alpha-formulas and beta-formulas, examples. A semantic tableau algorithm for solving the satisfiability problem in Propositional Logic: a tableau branch, an expanded, terminated branch / tableaux, a closed branch / tableau. Soundness and completeness of the tableau algorithm for solving the satisfiability problem.
  2. Introduction to first order logic (FOL). Syntax: predicate symbols, function symbols, terms, quantifiers, free and bound variables. Semantics: interpretation (structure), object assignments, model, basic semantic definition (BSD), satisfiability, logical consequence, validity, examples of FOL equivalences.
  3. How to prove logical consequence and logical equivalence using BSD: examples. Substitution in terms and in formulas, a term freely substitutable for a variable in a formula, substitution theorem.
     Reasoning in FOL using semantic tableau: gamma-formulas, delta-formulas, systematic construction of a tableau, examples. Godel's soundness and completeness theorem for FOL.
  4. Examples of constructing a systematic semantic tableau. Examples of counter-models for some satisfiable FOL formulas. Prenex normal form, Skolem normal form. Finitely axiomatizable theories, incomplete and complete theories: linear dense order. The satisfiability and entailment problems in FOL are undecidable (Church-Turing theorem). Compactness of FOL. A theory of single successor, its axiomatization, and models, including non-standard models.
     Limitations of FOL: transitive closure cannot be formulated in FOL. Second order logic: Syntax and semantics.
  5. Introduction to reasoning about action. Intuitive ontology for the situation calculus. The qualification problem: the precondition axioms as a tentative solution in FOL. Deterministic, primitive, atemporal actions without side-effects. Frame axioms (axioms about lack of effects for actions), the frame problem: Reiter's solution. Effect axioms, normal form for effect axioms. Transforming effect axioms for a given fluent into a single positive effect axiom and a single negative effect axiom for the fluent. Explanation closure, causal completeness assumption, successor state axioms.
  6. Foundational axioms for the situation calculus, the tree of situations. Principles of induction. Uniform formulas, regressable formulas. Basic action theories (BATs): precondition axioms, successor state axioms, initial theory, foundational axioms, unique name axioms (UNA). The projection and executability problems. Two techniques for solving these problems: regression (reasoning backwards) and progression (reasoning forward). The regression operator. The relative satisfiability theorem. The theorem about reducing the projection problem to entailment of a regressed formula from an initial theory (together with UNA).
  7. Data base update transactions formalized in the situation calculus. STRIPS assumption vs ADL theories vs arbitrary basic action theories. Implementing basic action theories in Prolog: closed world assumption (CWA), open world assumption (OWA). Domain Closure Assumption (DCA) vs open domains with possibly unspecified objects.
  8. Optimal planning: A* algorithm. Heuristics. The Planning Domain Definition Language (PDDL). State of the art planners. Translating from PDDL to CPS721 Prolog representation based on situations and fluents. The planning problem formulated as an entailment problem in the situation calculus. Advantages of this formulation.
  9. Reasoning about indirect effects of actions. Circumscription: general definition, circumscription with fixed and variable predicates, examples when circumscription can be expressed in FOL. State constraints, the ramification and qualification problems, the causality predicate, causal rules, compiling state constraints into successor state axioms.
  10. Actual causes in situation calculus. Motivation: token causality vs generic causality. Well-known examples of finding causes from a given scenario. Pearl and Halpern's structural causal models approach. Using basic action theory to represent domain dynamics. One-step regression for a formula representing an observed effect. Achievability cause, and the chain of achievability causes. Maintenance causes serve to mitigate risks associated with potential threats to an achieved effect. In a general case, actual causes recursively combine achievability and maintenance causes. Applications of causal analysis to computing the actual cause of a failure from a log of actions/events.
  11. Advanced topics in reasoning about action: time and concurrency. Instantaneous actions, processes extended in time. Approaches to axiomatizing concurrency. Natural actions: representing physical laws, least natural time point. Correct reasoning about hybrid systems. Diagnosis of failures in hybrid systems.
  12. (Optional topic, if time permits) Reasoning forward in the situation calculus. Forgetting about a single ground atom and about multiple ground atoms. Progression in the situation calculus. Local-effect basic action theories. Computing progression efficiently.
  13. (If time permits) Advanced topics in reasoning about action: stochastic actions. Markov Decision Processes (MDPs), decision theoretic (DT) planning. Decision-tree based methods to solving the DT-planning problem with a finite horizon. DT-Golog: problem representation, semantics, computing a policy and its value, sensing actions, on-line interpreter. Applications to robot programming and to requirements engineering.
  14. (If time permits) Taxonomies of actions: troponyms (the possible relations between verbs in the semantic network of the WordNet database). Computational advantages of taxonomies of actions. Successor state axioms using taxonomies of actions.

Course Policies

• The students are strongly encouraged to take notes in class, and study their notes after class. Learning can be a gradual process that requires time and efforts. The students benefit from attending lectures since some important details will be discussed only there. For this reason, attending lectures is mandatory.
• All course materials posted on D2L are copyrighted and protected by law. You cannot share them with anyone. You cannot repost them anywhere on the Web. Please review the University policy about copyrights. Moreover, you cannot upload or share in any way with anyone your solutions to homework assignments, since doing this would violate the CP8314 policy on collaboration, and the university Academic Policy 60. You can read parts of this policy online related to "Academic misconduct".
• The policy about electronic devices for in-person lecture delivery: turn off your mobile phones and all other electronic devices in class. You can keep your laptop or tablet open only if you use it to take notes in class.
• Examinations: There is a midterm test, but no final exam. The midterm test focuses on the concepts, algorithms and concepts covered in the 1st, 2nd and 3rd homework. Grades are earned for the demonstration of knowledge. All documentation related to special accommodation or academic consideration should be submitted to the CS program office within the specified time limits.


• Dates are subject to change, all changes will be announced in class and on the course Web pages.
• Assignments should be submitted to a specified folder on D2L before the deadline specified in the homework assignment (you are encouraged to submit assignments earlier). Your assignment is considered late if any part of the assignment is late and the penalty for a late assignment is 25% off. No assignments will be accepted if more than 24 hours late. Start solving your assignment on the same day when it is posted. Do not procrastinate. No make-up assignments.
• From time to time, I will hand out exercises. The students are expected to solve the exercises, but they will not be graded. However, working on exercises will improve your understanding of this course and will help you to get better marks on tests.
• Up to 5% extra credit may be assigned for class participation, e.g., a student attends the entire class, participates actively by asking/answering questions, works on problems in class and/or attends office hours. Class participation marks are earned for active course participation and given at discretion of the course instructor; they cannot be requested by the students.
• Handouts and assignments will be made available on the Web only. You are responsible for visiting the course Web pages regularly and reading assignments related information that is provided or linked from these Web pages. Before sending your questions by e-mail to the instructor, check these Web pages whether similar questions have been already answered.
• Email communication: please send me email from local university email addresses only. Please be aware that email sent from external popular email servers can be filtered out as spam and might not reach me. Email messages will be normally answered within 24 hours. However, messages sent on weekend (starting from Friday late afternoon) will be usually answered on Monday.
• Grades for tests and assignments will be posted electronically no later than two weeks after the due date (test date).

ACADEMIC MISCONDUCT
Committing academic misconduct, such as plagiarism and cheating, will trigger academic penalties including failing grades, suspension and possibly expulsion from the University. As a Ryerson student, you are responsible for familiarizing yourself with the Student Code of Academic Conduct.

Contract Cheating Statement
In regard to any and all assessments in this course, the use of Chegg or any other similar help site/service will be pursued as "contract cheating".

In regard to any and all assessments in this course, the use of any third party (e.g., family member, freelancer, roommate, friend, tutor) to complete work on your behalf will be pursued as "contract cheating" under Policy 60 "Academic Integrity".

Policy 60 Penalty Guidelines for contract cheating (e.g., viewing a solution on Chegg or Discord) that only impacts you: F in course.

Policy 60 Penalty Guidelines for contract cheating that facilitates cheating for others (e.g., posting a question to Chegg): Disciplinary Suspension.

Policy on Non-Academic Conduct
No disruption of instructional activities is allowed. In particular, taking video/photos in class is strictly prohibited since this violates the copyright and privacy policies. Among many other infractions, the Code specifically refers to the following as a violation: ``Disruption of Learning and Teaching - Students shall not behave in disruptive ways that obstruct the learning and teaching environment." In particular, the students can use the laptops (and similar electronic devices) in class only for taking notes. In order to create an environment conducive to learning and respectful of others rights, phones and pagers must be silenced during lectures. Students should refrain from arriving late and/or leaving the classroom before the lecture is finished. In difficult cases, penalties can be imposed by the Student Conduct Officer.

Remarking Policy

1. Grades are earned for the demonstration of knowledge.
2. You canot request remarking or recalculation later than TEN DAYS from the date on which your mark was posted.
3. Mark can decrease or remain the same if a marker finds something that was incorrectly awarded too high a mark.

Tentative Course Calendar (subject to change: all changes will be announced in class)

Course Work	Due Date	Grade Value (%)
Assignment  1 (in two parts)	September 12 and September 19	5%
Assignment 2 (in two parts)	September 26 and October 3	5%
Assignment 3	October 24	5%
Midterm Exam (in class)	October 25, 2022	25%
Assignment 4	November 14	5%
Assignment 5	November 21	5%
Project Proposal	November 23	5%
In-class presentation (topics to be provided)	November 29	15%
Course Project Report	December 12, 2022	30%
		100%