PPT-Deductive Verification Tools

Tutorial for Dagstuhl Seminar 16201 18 th May 2016 Alexander J Summers ETH Zurich Switzerland while i gt0 i . In a deductive argument the premises are intended to provide support for the conclusion that is so strong that if the premises are true it would be impossible for the conclusion to be false An inductive argument is an argument in which it is thought Deductive reasoning. , also . deductive logic. or . logical deduction. or, informally, . ". top-down. " logic. , is the process of . reasoning. from one or more . statements. (premises) to reach a logically certain conclusion. It differs from . Arguments. Premise: . statement upon which an argument is based or from which a conclusion is drawn. Premise is either true or false. Arguments: . Consist of one or more premises and one conclusion or claim, which is drawn from those premises. It’s Logical. What is Logic?. Logic. – The science of correct reasoning.. Reasoning. . – The drawing of inferences or conclusions from known or assumed facts. .. There are two main types of reasoning:. TOK. Lecture 7: Ways of Knowing - Reason. Part 1: What is reasoning? And, how does it lead to knowledge?. What is reasoning?. A possible answer: reasoning is the mental processing of information.. But, not all mental processing. Section 2.3. : . Using . deductive reasoning to verify conjectures. Chapter 2: Geometric Reasoning. I Can. Determine whether inductive of deductive reasoning is being used for a given scenario.. Apply the Law of Detachment in logical reasoning and determine if it is being used validly.. A Framework for Audience Analysis. Background. Logic has been a formal academic discipline for almost 2,500 years. The 4th century B.C.E. Greek philosopher Aristotle first systematized formal logic, and university logic courses teach Aristotelian logic to this day. For much of western history, logic was one of the main branches of schooling (the classical curriculum consisted of grammar, logic and rhetoric). With the growth of more specialized disciplines and wider curricula in the 20th century, formal logic got lost in the shuffle. In its place, philosophers began formulating courses in what we now call critical thinking, or informal logic. Formal rules and the reduction of sentences to things like. FOCUS UP!!. BUCKLE DOWN!!. TRY NOT TO BE ABSENT!!. WORK HARD!. GET REST!. This is a marathon…. not a sprint…. You after EOC. Our Plan of Attack. Mini lessons. Item sampler practice test and review. VS. . Inductive . Reasoning. Aristotle. . (Ancient Greek Philosopher). Start with a . premise. Premises lead to a . certain. conclusion. DEDUCTIVE REASONING. Sir Francis Bacon. (17. th. Century English Philosopher). Thinking Mathematically. Objectives. Understand mathematical reasoning . Distinguish between inductive and deductive reasoning . Identify . arithmetic and geometric sequences . Thinking Mathematically. Induction vs Deduction. Fogelin. and . Sinnott. -Armstrong describe the difference between induction and deduction as follows:. Deductive arguments are intended to be valid. Inductive arguments are not intended to be valid but still to provide a reason for the conclusion. Verification is confirmation of eligibility for free and reduced price meals under NSLP and SBP. . Verification is . not . required for CEP schools or DC students. . Verification activities begin on Oct. 1 and must be concluded by November. To form conjectures through inductive reasoning. To disprove a conjecture with a counterexample. To avoid fallacies of inductive reasoning. Example 1. You’re at school eating lunch. You ingest some air while eating, which causes you to belch. Afterward, you notice a number of students staring at you with disgust. You burp again, and looks of distaste greet your natural bodily function. You have similar experiences over the course of the next couple of days. Finally, you conclude that belching in public is socially unacceptable. The process that lead you to this conclusion is called. Note-Taking Guide. I suggest only writing down things written in . red. Inductive vs. Deductive Reasoning. What was our definition of inductive reasoning (section 2.1)?. Process of looking for patterns, making a conjecture, and then attempting to prove the conjecture true or false.