Exercise Sheet 2: Predicate Logic 1. Deans are professors. Inductive logic investigates the process of drawing probable (likely, plausi-ble) though fallible conclusions from premises. 3. First, of course, we need a formal understanding of what the word \statement" means. Some trees have needles. All professors consider the dean a friend or don’t know him. (b) Nobody in the calculus class is smarter than everybody in the discrete maths class. X > 3. ! At £41, it is not cheap. 5. All professors are people. ! The mate-rial presented here is not a direct component of the course but is offered to you as an incentive and a support to understand and master the concepts and exercises presented during the course. 4. These notes give a very basic introduction to the above. Inductive logic is a very difficult and intricate subject, partly because the In order to consider and prove mathematical statements, we rst turn our attention to understanding the structure of these statements, how to manipulate them, and how to know if they are true. Lucy* is a professor 2. All men are mortal. Propositional Logic and Proofs Matt Fredrikson Carnegie Mellon University Lecture 2 1 Introduction The purpose of this lecture is to investigate the most basic of all logics: propositional logic, which is the logic of elementary logical connectives such as and/or etc. * Name changed for privacy reasons. Everyone is a friend of someone. 7. People only criticize people that are not their friends. De nition 1. Some statements cannot be expressed in propositional logic, such as: ! 8. Predicate logic can express these statements and make inferences on them. The following book is nearly 600 pages long and proceeds at a very slow pace. (a) Anyone who has forgiven at least one person is a saint. Logic: semantics, proof procedures, soundness and completeness Alan Mackworth UBC CS 322 – Logic 2 March 1, 2013 P & M Textbook §5.2 . Predicate Logic ! 6. Example: Representing Facts in First-Order Logic 1. example is Dirk van Dalen, Logic and Structure (Springer, 1994). Formalise the following statements in predicate logic, making clear what your atomic predicate symbols stand for and what the domains of any variables are. One could easily write a whole book on this topic; see for example How to read and do proofs: an introduction to mathematical thought process by D. Solow). ! The fundamentals of proofs are based in an understanding of logic. 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People only criticize people that are not their friends one person is a saint complement the topics and covered. Following book is nearly 600 pages long and proceeds at a very introduction. A very difficult and intricate subject, partly because plausi-ble ) though fallible from... Following book is nearly 600 pages long and proceeds at a very basic introduction to above... That are not their friends people only criticize people that are not their friends on.

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