Temporal logic a logic for specifying properties over time e. The term logic model often is used interchangeably with other names similar in concept blueprint, causal chain, conceptual map, model of change, roadmap, theory of action, and theory of change. If we seek help by deciding that no class is a member of itself, then w becomes the class of. Unit 1 set theory and logic notes booklet unit 1 set theory and logic worksheet booklet unit 1 set theory and logic worksheet answers foundations 30 unit 1 portfolio lesson 1 types of sets and set notation lesson 1 video homework. Use of logic models and theory of change models for planning. Our development of set theory will involve both types of investigations indicated above. There is no algorithm or specific way to write a proof, so what you write should be an expression of your thought processes and logic. These notes were prepared using notes from the course taught by uri avraham, assaf hasson, and of course, matti rubin. Proof, sets, and logic department of mathematics boise state. Introduction to logic and set theory 202014 general course notes december 2, 20 these notes were prepared as an aid to the student. A set of sentences in a formal language is one of the components that form a theory. These notes are not endorsed by the lecturers, and i. The term logic model often is used interchangeably with other names similar in concept blueprint. The exciting and active areas of logic today are set theory, model theory and connections with computer science.
We will need only a few facts about sets and techniques for dealing with them, which we set out in this section and the next. A logic model that is a summary of an underlying theory is a much more powerful tool. In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. In mathematics, the notion of a set is a primitive notion. Logic models are an iterative tool useful for planning and evaluation purposes. A equals b,written ab,iff every element of a is also an element of b,and conversely,every element of b is also an element of a. Herbert kenneth kunen born august 2, is an emeritus professor of mathematics at the university of wisconsinmadison who works in set theory and its. A logic model is a graphic or visual depiction that summarizes key elements of a toc, and it is often used as a facilitation tool during the design process. Any object which is in a set is called a member of the set. Introduction to logical theory by peter frederick strawson. Introduction to logic and set theory202014 general course notes december 2, 20 these notes were prepared as an aid to the student. Developing a theoryof change logic model for your program w. The objects of study are models of theories in a formal language.
Logic and set theory virginia commonwealth university. When you put your reasoning into words, you produce what logicians call an argument. Logical theory definition of logical theory by the free. The key to the whole project is a new axiom of set theory which i dubbed the law of extremes. Mathematical logic is a branch of mathematics which is mainly concerned with the relationship between semantic concepts i. Choi kaist logic and set theory september 23, 2011 1 38. If iias build on the existing early college high school model and require key partnerships among high schools, regional employers and industry, and two and fouryear universities, then students will have opportunities to acquire dual credit, certifications, and. The fundamental tenet of model theory is that mathematical truth, like all truth, is relative. Set theory for computer science pdf department of computer. Introduction to logic and set theory 202014 bgu math. Mar 14, 2016 the toc gives the big picture and summarises work at a strategic level, while a logical framework illustrate a programme implementation level understanding of the change process.
Paper 2, section ii 16g logic and set theory state and prove the knastertarski fixedpoint. Basic logic volume 1 is a brief study of the other three areas of logic mentioned above. Bratton centered his attention on the new york subways, and reinvigorated the subway police. In chapter 14 we present scott and solovays notion of boolean. The period from the 1930s thru the 1970s saw great progress in logic. However, according to millar et al,2 logic models that begin with the inputs and work through to the desired outcomes may reflect a natural tendency to limit ones thinking to existing activities, programs, and research questions. It aims to scratch the tip of the surface of the philosophy of set theory. One must demonstrate that a proposition is true in all cases before it is considered a theorem of. Set theory and logic supplementary materials math 103. The axiom of pair, the axiom of union, and the axiom of. When you put your reasoning into words, you produce what logicians call an. An elementary introduction to logic and set theory. Quines introduction to abstract set theory and to various axiomatic.
We restrict our attention to socalled first order theories, that is, those axiomatic theories for which the predicate. Use of logic models and theory of change models for. Ellermeyer august 18, 2000 set theory membership a setis a welldefined collection of objects. Chapter 1 logic and set theory to criticize mathematics for its abstraction is to miss the point entirely. Oleary, the structure of proof with logic and set theory, 2002. Simply put, logic models graphically describe the theoryor logicof how a program is supposed to work. Propositional logic, interpretation with respect to a. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Mathematical logic as based on the theory of types. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools. It assumes no knowledge of logic, and no knowledge of set theory beyond the vague familiarity with curly brackets, union and intersection usually expected of an advanced mathematics. The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. No student is expected to really benefit from these notes unless they have regularly attended the lectures. In mathematics, model theory is the study of classes of mathematical structures e.
Leader, lentterm 2005, 2010 chapter 1 propositional logic 1 chapter 2 wellorderings and ordinals 7 chapter 3 posets and zorns lemma 16 chapter 4 predicate logic 24 chapter 5 set theory 34 chapter 6 cardinals 43. An argument, as the word is used in logic and in intellectual contexts generally, is reasoning that has been put into words. If the object x is a member of the set a, then we write x a which is read as x is a member of aorx belongstoaorx is in aorx is an. The various subfields of this area are connected through their study of foundational notions. Notes on set theory, logic, and computation alexander a. Set theory and logic dover books on mathematics reprint. It remains to mention some of the ways in which people have spoken misleadingly of logical form. Pdf second order logic, set theory and foundations of. It allows for quick proofs of basic settheoretic identities and logical tautologies, so it is also a good tool to aid ones memory. The logic model process has been used successfully following the above sequence. In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of zermelofraenkel set theory.
This is the point where an author usually apologizes for what has been omitted. Logical theory synonyms, logical theory pronunciation, logical theory translation, english dictionary definition of logical theory. If a theory is axiomatisable by a set s of sentences, and also by a nite set t of sentences, does it follow that the theory is axiomatisabl e by some nite subset of s. It only remains to define a, b in terms of set theory. Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms.
An overview of broken windows theory the early 1990s in new york city greeted william bratton as the new commissioner of the new york police department. Choi department of mathematical science kaist, daejeon, south korea fall semester, 2011 s. It is designed for a onesemester course in set theory at the advanced undergraduate or beginning graduate level. They are not guaranteed to be comprehensive of the material covered in the course. We have placed it after basic logic models because. Witno, discrete structures in five chapters, 2010, createspace. One of the commonest of these is to talk of the logical form of a statement. Logic and set theory year 2019 2018 2017 2016 2015 2014 20 2012 2011 2010 2009 2008 2007 2006 2005. The toc gives the big picture and summarises work at a strategic level, while a logical framework illustrate a programme implementation level understanding of the change process. Students need to be familiar with the following concepts. A equals b,written ab,iff every element of a is also an element of b, and conversely,every element of b is also an element of a. For example, a deck of cards, every student enrolled in. For example, a deck of cards, every student enrolled in math 103, the collection of all even integers, these are all examples of sets of things.
Like logic, the subject of sets is rich and interesting for its own sake. The most basic form of logic is propositional logic, which concerns itself with ways of combining propositions using words such as \and, \or, \if. Summarize your theory in ways that serve the purposes of your different constituents, such as residents, funders, boards, etc. Set theory and its logic by willard van orman quine. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the power sets. This book is designed for readers who know elementary mathematical logic and axiomatic set theory, and who want to learn more about set theory. Unit 1 set theory and logic miss douglas class website. Mathematical logic investigates the power of mathematical reasoning itself. It is possible to have a 11 correspondence between an in. Differences between the theory of change and the logic model. Math 522, advanced set theory, at boise state university, on the. The set theory work to this point is selfcontaine d, given a knowledge of the godel consistency proof 4, i n more detail 3.
If we seek help by deciding that no class is a member of itself, then w becomes the class of all classes, and we have to decide. William weiss and cherie dmello university of toronto. Although it will touch most of the themes of that part ii course, and will have something of the character of a course with a title like a twentyfour. This howto note describes considerations for developing a project logic model, as well as steps for thinking through a more complete theory of change toc. Leader, lentterm 2005, 2010 chapter 1 propositional logic 1 chapter 2 wellorderings and ordinals 7 chapter 3 posets and zorns lemma 16 chapter 4 predicate logic 24 chapter 5 set theory 34 chapter 6 cardinals 43 bonus lecture incompleteness examples sheets prerequisites.
In most cases, if you are developing a new program, this step should come first to inform your preliminary thinking. Curiously, set theory arose in the context of sets of real numbers related to the convergence of fourier series. Notes,whiteboard,whiteboard page,notebook software,notebook,pdf,smart,smart technologies ulc,smart board. Mit was a major center in the field from the 1950s through the 1980s. The introduction to nlp module assumes some basic knowledge of set theory and logic. We will return to sets as an object of study in chapters 4 and 5. Logical theory begins with the concept of an argument. This is being written as a textbook for math 502, logic and set theory, and. Set theory and logic is the result of a course of lectures for advanced undergraduates, developed at oberlin college for the purpose of introducing students to the conceptual foundations of mathematics. Basic set theory and logic university of cambridge. The basic idea of a set, set intersection, set union etc. In 1829, dirichlet had shown that a function always had a fourier series converging to itself, under certain sufficient conditions he considered periodic functions with finitely many extrema in every period and equal to the halfsum of.
Exercise 3 guides you through a series of six steps that diagram the fundamental theory that supports your program. In other words, the logical framework is like a microscopic lens that zooms in on a specific pathway within the toc. That is, a proof is a logical argument, not an empir. As opposed to predicate calculus, which will be studied in chapter 4, the statements will not have quanti er symbols like 8, 9. Infinite cardinals are treated anew in clearer and this is an extensively revised edition of mr. This supports and builds upon the basic logic model. The solution that is most commonly used in mathematics is an axiomatic theory known as zermelofraenkel zf set theory, which has among other axioms an axiom of foundation, which e ectively implements the. Select the letter of the most appropriate answer and shade in the corresponding. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory. Model theory is the part of mathematics which shows how to apply logic to the study of structures in pure mathematics. Set theory and logic thomas forster this course is the sequel to the part ii course with the title logic and set theory. When we say \ppis a correct, there are two ways we can. That is, a proof is a logical argument, not an empir ical one.
1122 133 295 252 626 605 1010 1495 1251 901 964 994 1304 81 860 397 147 720 1063 762 493 656 1137 110 1098 373 520 662 1076 226 1346 1367 738 1133 554 551 540 114