Problems on propositional logic, including truth-tables, boolean algebra, and inference rules.

An introduction to reasoning with Proposition and First-order logic, with applications to computer science. Part of the TeachLogic Project (www.teachlogic.org).

We saw three stages of logics: Propositional logic, with formulas like ? Predicate logic, where the same statement was phrased as ?. This introduced the idea of variables, which ranged over atomic propositions. First-order logic, which included quantifiers; the above statements were superceded with the likes of ?. So why, you might ask, didn't we just start out with first-order logic in the first lecture? One reason, clearly, is to introduce concepts one at a time: everything you needed to know about one level was needed in the next, and then some. But there's more: by restricting our formalisms, we can 't express all the concepts of the bigger formalism, but we can have automated ways of checking statements or finding proofs. In general, this is a common theme in the theory of any subject: determining when and where you can (or, need to) trade off expressibility for predictive value. For example, ? Linguistics: Having a set of precise rules for (say) Tagalog grammar allows you to determine what is and isn't a valid sentence; details of the formal grammar can reveal relations to other languages which aren't otherwise so apparent. On the other hand, a grammar for any natural language is unlikely to exactly capture all things which native speakers say and understand. If working with a formal grammar, one needs to know what is being lost and what is being gained. Dismissing a grammar as irrelevant because it doesn't entirely reflect usage is missing the point of the grammar; Conversely, condemning some real-life utterances as ungrammatical (and ignoring them) forgets that the grammar is a model which captures many (if not all) important properties. Of course, any reasonable debate on this topic respects these two poles and is actually about where the best trade-off between them lies. Psychology: Say, Piaget might propose four stages of learning in children. It may not trade off total accuracy, for (say) clues of what to look for in brain development. Physics: Modern pedagogy must trade off quantum accuracy for Newtonian approximations. Researchers exploring fields like particle physics must trade off exact simulations for statistical ("stochastic") approximations. Understanding the theoretical foundations of a field is often critical for knowing how to apply various techniques in practice.

This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. The book is self contained, and the level corresponds to senior undergraduates and first year graduate students. However, there is enough material for at least a two semester course, and some Chapters (Chapters 6,7,9,10) contain material which could form the basis of seminars. It would be helpful, but not indispensable, if the reader has had an undergraduate-level course in set theory and/or modern algebra.

This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information technology, and graduate (16.413) students.

A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.

The domain axioms for WaterWorld in propositional logic.