Logic Guide (Rev

Total Page:16

File Type:pdf, Size:1020Kb

Logic Guide (Rev Logic Guide www.ti.com/logic 2017 Logic Guide Introduction and Contents Introduction Today’s applications are evolving with greater functionality and smaller size. Table of Contents As the world leader in logic, Texas TI’s goal is to help designers easily find Logic Guide 2017 Instruments (TI) offers a full spectrum the ideal logic technology or function 2 Introduction and Contents of logic functions and technologies they need. Logic families are offered at that range from the mature bipolar and Logic Overview every price/performance node along bipolar complementary metal-oxide 3 World of TI Logic with benchmark delivery, reliability, and semiconductor (BiCMOS) families to 4 IC Basics worldwide support. TI maintains a firm the latest advanced-CMOS families. TI commitment to remain in the market 5 Automotive Logic offers process technologies with the with both leading-edge and mature 6 Introducing the Next Generation logic performance and features needed QFN packaging logic lines. in today’s electronic markets while 7 Technology Functions Matrix maintaining support for traditional logic Logic suppliers have historically focused Logic Families products. on speed and low power as the priori- ties for product family improvement. As 8 AUC TI’s product offerings include the shown below, improved performance is 8 AUP following process technologies or device offered by many new TI product tech- 9 ALVC families: nologies such as AUC (1.8 V) and ALVC 9 AUP1T • AC, ACT, AHC, AHCT, ALVC, AUC, (3.3 V) depending on operating voltage 9 AVC AUP, AVC, FCT, HC, HCT, LV-A, LV-AT, requirements. Other technologies such 10 LV1T/LV4T LVC, TVC as AUP focus on delivering “best-in- 10 LVC/LVC1G • ABT, ABTE, ALB, ALVT, BCT, HSTL, class” low-power performance. 11 AC/ACT LVT, LV1T, LV4T 11 AHC/AHCT • FB, VME Data sheets can be downloaded from 11 HC/HCT • ALS, AS, F, LS, S, TTL the TI Web site at www.ti.com or ordered through your local sales office or TI 12 LV-A/LV-AT authorized distributor. (See back cover.) 12 ALB 12 ALVT 13 LVT CMOS Voltage vs. Speed 13 ABT/ABTE 13 ALS/AS/S/LS 25 14 BCT HC 14 F AHC 15 FCT 20 15 TTL AC 15 CD4000 LVA (ns) pd LVC Resources t 15 , ALVC 16 Package Options AVC 17 Related Logic Resources 19 TI Worldwide Technical AUC 10 Support 5 Typical Propagation Delay Typical 0 01234567 CMOS Voltage, VCC (V) Texas2 | Logic Instruments Guide 2017 LogicTexas Guide Instruments 2017 | 2 Logic Overview World of TI Logic Some logic families have been in the marketplace for years, the oldest is well into its fifth decade. The following section gives the logic user a visual guide to the technology families that are available and their optimal voltage levels. 0.8-V Logic 1.2-V Logic 1.5-V Logic AUC, AUP AUC, AUP, AVC AUC, AUP, AVC 1.8-V Logic 2.5-V Logic 3.3-V Logic ALVC, AUC, AUP, AVC, LVC, LV1T ALVC, ALVT, AUC, AUP, AVC, AC, AHC, ALB, ALVC, ALVT, LV, LV1T, LV-A, LVC AUP, AVC, LV, LV-A, LVC, LVT, LV1T, AUP1T 5-V Logic ABT, AC/ACT, AHC, AHCT, ALS, AS, BCT, F, LV, LV1T, LV-A, LS, S, TTL, CD4000, FCT2 5-V+ Logic CD4000 Texas Instruments Logic Guide 2017 | 3 Logic Overview IC Basics: Comparison of Switching Standards Shown below are the switching input/ Is VOH higher than VIH? output comparison table and graphic Is VOL less than VIL? that illustrate VIH and VIL, which are the minimum switching levels for guaranteed operation. Vt is the approximate switching DR level and the VOH and VOL levels are the guaranteed outputs for the VCC specified. R5 TTL 5 CMOS 3 LVTTL 2.5 CMOS 1.8 CMOS D 5 TTL Yes No Yes* Yes* Yes* 5 CMOS Yes Yes Yes* Yes* Yes* 3 LVTTL Yes No Yes Yes* Yes* 2.5 CMOS Yes No Yes Yes Yes* 1.8 CMOS No No No No Yes* * Requires VIH Tolerance 5 VVCC 5 VVCC 4.44 VOH 3.5 VIH 3.3 VVCC 2.5 Vt 2.5 VVCC 2.4 VOH 2.4 VOH 2.3 VOH 1.8 VVCC 2.0 VIH 2.0 VIH 1.7 VIH 1.5 V 1.5 V 1.2 V t IL 1.5 Vt OH 1.17 VIH 1.2 Vt 0.9 Vt 0.8 VIL 0.8 VIL 0.0 VIL 0.7 VIL O.5VOL 0.4 VOL 0.4 VOL 0.45 VOL 0.2 VOL 0 GND 0 GND 0 GND 0 GND 0 GND 5-V TTL 5-V CMOS 3.3-V LVTTL 2.5-V CMOS 1.8-V CMOS Standard TTL: ABT, Rail-to-Rail 5 V LVT, LV1T, LV4T, AUC, AUP, AVC, AUC, AUP, AVC, AHCT, HCT, ACT, HC, AHC, AC, LV-A, LVC, ALVC, AUP, ALVC, LVC, ALVT, ALVC, LVC, bipolar, LV1T, LV4T LV1T, LV4T LV-A, ALVT LV1T, LV4T LV1T, LV4T Texas4 | Logic Instruments Guide 2017 LogicTexas Guide Instruments 2017 | 4 Logic Overview Automotive Logic Texas Instruments (TI) offers a vast port- Package Offerings includes quality-control checks geared folio of automotive logic products that TI’s packaging options for logic products to achieve the zero-DPPM requirements are compliant to the AEC-Q100 standard. range from standard SOIC and TSSOP of automotive OEMs. These devices are applicable for automo- packages to small-form-factor SC70 and Reliability tive, industrial, and high-reliability systems SOT-23 packages. These logic products TI’s design-flow checks ensure that and come with world-class support. are suitable for a wide spectrum of auto- all automotive logic products meet or motive applications. Breadth of Product Functions exceed long-term reliability expectations. TI’s automotive logic products include Benchmark Lead Times Supply Continuity a wide range in functionality in both With a vast network of worldwide wafer TI has a solid track record of supply standard logic and little logic functions fabs and assembly/test sites, TI supports continuity. TI’s first logic products such as single-, dual- and triple-gates. automotive customers with benchmark were introduced in 1964 and are still in With more than 125 different standard product lead times. Most TI automotive production and supported. Automotive gate functions and close to 40 little logic logic product lead times are six weeks grade products have been in production functions, TI has one of the most compre- or less. hensive portfolios for automotive logic and supported since 1984. in the industry. This gives automotive Quality Control For the full list of TI’s automotive logic system designers the flexibility to choose All logic products go through a tightly products, please visit www.ti.com/logic the functions they need for their target controlled manufacturing process that systems. Start Your Future Automotive Designs with TI Logic Texas Instruments Logic Guide 2017 | 5 Logic Overview Introducing the Next Generation QFN Packaging New Packaging for Space-Constrained Applications TI’s premier packaging portfolio allows for logic devices to be incorporated into small form factors such as the ever-shrinking wear- ables, mobile devices, home automation, as well as healthcare and fitness devices. Any customer planning to fit advanced logic functions into space constrained applications will find the X1QFN and X2SON packages to be a valuable resource for new designs. X1QFN X1QFN is a new advanced packaging series available for 14-, 16-, and 20-pin devices offered by Texas Instruments (TI) with a lower propagation delay and wider operating temperature than any 20 PDIP other QFN package. The 14-pin X1QFN (N) 52% is just 2.5 x 2.1 x 0.5 mm with 0.4-mm QFN 20-pin Smaller X1QFN 20-pin pitch, a major revolution in the industry 20 SOIC 4.5 x 3.5 mm 3.3 x 2.5 mm (DW) (RGY) (RWP) for small-scale packages. Such small package sizes were previously only 20 SOP (NS) offered for little logic functions such as 20 QSOP single-, dual- and triple-gates, but with (DBQ) 44% QFN 16-pin Smaller X1QFN 16-pin aggressive die shrinking, TI has brought 4 x 3.5 mm 2.5 x 2.5 mm 20 TVS0P (RGY) (RWN) multi-gate functions to this advanced (DGV) 20 TSSOP small-scale package. (PW) 16 QSOP 16 SSOP (DBQ ) (DB) 16 TSSOP (PW) 16 TVSOP (DGV) X2SON TI is not only investing in standard logic space, but also in popular little logic functions. TI has released the newest and smallest next generation X2SON package (a.k.a. X2QFN) for 5-pin and 6-pin devices. The 5-pin DPW package QFN (DRY) X2SON 5-pin is just 0.8 x 0.8 x 0.4 mm (0.5-mm pitch), 0.8 x 0.8 mm whereas the 6-pin DTB package is only (DPW) Actual Size 0.8 x 1.0 x 0.4 mm (0.4-mm pitch). Smaller X2SON 6-pin 0.8 x 1.0 mm (DTB) X2SON (DSF) 22 to 36% Smaller 6 | Logic Guide 2017 Texas Instruments Logic Overview Technology Function Matrix Functions Special Features Process (Partial (Partial OFF Power Down) Power Schmitt Triggers Overvoltage- tolerant Inputs Power-off Output Disable 3-State Power-up Bipolar CMOS BiCMOS Families Voltage Buffers/Line Drivers Configurable Logic Flip-Flops Combination Logic Counters Shift Registers Encoders/ Decoders Digital Comp/ Gen. Parity Gates Transceivers Level Translators Phase Lock Loops Bus-Hold Series Damping Resistors I AUC 0.8, 1.8, 2.5 4 4 4 4 4 4 4 4 4 4 4 AUP 0.8, 1.8, 3.3 4 4 4 41 4 4 4 41 41 41 ALVC 1.8, 3.3 4 4 4 4 4 4 4 4 4 4 AUP1T 1.8, 3.3 4 4 41 4 4 41 41 41 AVC 1.8, 3.3 4 4 4 41 4 4 4 41 41 41 LV1T 1.8, 3.3, 5 4 4 4 4 4 4 LVC 1.8, 3.3, 5 41 41 41 41 41 4 4 41 4 4 4 41 41 41 4 41 AC 3.3, 5 41 4 4 4 4 41 4 4 4 41 AHC 3.3, 5 41 41 41 4 41 41 4 4 41 41 HC 3.3, 5 41 41 41 41 41 4 41 4 4 4 4 41 LV-A 3.3, 5 41 41 41 41 4 4 4 4 4 4 4 41 41 41 ALB 3.3 4 4 4 ALVT 3.3 4 4 4 4 4 4 4 4 4 GTL 3.3 4 4 4 4 4 GTLP 3.3 4 4 4 4 4 4 4 4 LVT 3.3 41 4 41 41 4 4 41 4 41 VME 3.3 4 4 4 4 4 4 ABT 5 41 4 4 4 4 4 41 41 41 ABTE 5 4 4 ACT 5 41 41 4 4 4 4 41 4 4 4 4 4 41 AHCT 5 41 41 4 41 41 4 4 4 41 41 ALS 5 4 4 4 4 4 4 4 4 4 AS 5 4 4 4 4 4 4 4 4 4 BCT 5 4 4 4 4 4 4 F 5 4 4 4 4 4 4 4 4 4 4 FB 5 4 4 4 FCT 5 4 4 4 4 4 4 4 4 4 HCT 5 41 41 4 4 4 4 4 4 4 4 41 LS 5 4 4 4 4 4 4 4 4 4 4 4 LV-AT 5 4 4 4 4 4 4 4 S 5 4 4 4 4 4 4 4 4 4 4 4 TTL 5 4 4 4 4 4 4 4 4 CD4000 5, 10, 12 to 18 41 4 4 4 4 41 4 4 41 41 4 4 41 1Also available
Recommended publications
  • Logic in Action: Wittgenstein's Logical Pragmatism and the Impotence of Scepticism
    This is the final, pre-publication draft. Please cite only from published paper in Philosophical Investigations 26:2 (April 2003), 125-48. LOGIC IN ACTION: WITTGENSTEIN'S LOGICAL PRAGMATISM AND THE IMPOTENCE OF SCEPTICISM DANIÈLE MOYAL-SHARROCK UNIVERSITY OF GENEVA 1. The Many Faces of Certainty: Wittgenstein's Logical Pragmatism So I am trying to say something that sounds like pragmatism. (OC 422) In his struggle to uncover the nature of our basic beliefs, Wittgenstein depicts them variously in On Certainty: he thinks of them in propositional terms, in pictorial terms and in terms of acting. As propositions, they would be of a peculiar sort – a hybrid between a logical and an empirical proposition (OC 136, 309). These are the so-called 'hinge propositions' of On Certainty (OC 341). Wittgenstein also thinks of these beliefs as forming a picture, a World-picture – or Weltbild (OC 167). This is a step in the right (nonpropositional) direction, but not the ultimate step. Wittgenstein's ultimate and crucial depiction of our basic beliefs is in terms of a know-how, an attitude, a way of acting (OC 204). Here, he treads on pragmatist ground. But can Wittgenstein be labelled a pragmatist, having himself rejected the affiliation because of its utility implication? But you aren't a pragmatist? No. For I am not saying that a proposition is true if it is useful. (RPP I, 266) Wittgenstein resists affiliation with pragmatism because he does not want his use of use to be confused with the utility use of use. For him, it is not that a proposition is true if it is useful, but that use gives the proposition its sense.
    [Show full text]
  • Logic Model Workbook
    Logic Model Workbook INNOVATION NETWORK, INC. www.innonet.org • [email protected] Logic Model Workbook Table of Contents Page Introduction - How to Use this Workbook .....................................................................2 Before You Begin .................................................................................................................3 Developing a Logic Model .................................................................................................4 Purposes of a Logic Model ............................................................................................... 5 The Logic Model’s Role in Evaluation ............................................................................ 6 Logic Model Components – Step by Step ....................................................................... 6 Problem Statement: What problem does your program address? ......................... 6 Goal: What is the overall purpose of your program? .............................................. 7 Rationale and Assumptions: What are some implicit underlying dynamics? ....8 Resources: What do you have to work with? ......................................................... 9 Activities: What will you do with your resources? ................................................ 11 Outputs: What are the tangible products of your activities? ................................. 13 Outcomes: What changes do you expect to occur as a result of your work?.......... 14 Outcomes Chain ......................................................................................
    [Show full text]
  • Introduction to Philosophy. Social Studies--Language Arts: 6414.16. INSTITUTION Dade County Public Schools, Miami, Fla
    DOCUMENT RESUME ED 086 604 SO 006 822 AUTHOR Norris, Jack A., Jr. TITLE Introduction to Philosophy. Social Studies--Language Arts: 6414.16. INSTITUTION Dade County Public Schools, Miami, Fla. PUB DATE 72 NOTE 20p.; Authorized Course of Instruction for the Quinmester Program EDRS PRICE MF-$0.65 HC-$3.29 DESCRIPTORS Course Objectives; Curriculum Guides; Grade 10; Grade 11; Grade 12; *Language Arts; Learnin4 Activities; *Logic; Non Western Civilization; *Philosophy; Resource Guides; Secondary Grades; *Social Studies; *Social Studies Units; Western Civilization IDENTIFIERS *Quinmester Program ABSTRACT Western and non - western philosophers and their ideas are introduced to 10th through 12th grade students in this general social studies Quinmester course designed to be used as a preparation for in-depth study of the various schools of philosophical thought. By acquainting students with the questions and categories of philosophy, a point of departure for further study is developed. Through suggested learning activities the meaning of philosopky is defined. The Socratic, deductive, inductive, intuitive and eclectic approaches to philosophical thought are examined, as are three general areas of philosophy, metaphysics, epistemology,and axiology. Logical reasoning is applied to major philosophical questions. This course is arranged, as are other quinmester courses, with sections on broad goals, course content, activities, and materials. A related document is ED 071 937.(KSM) FILMED FROM BEST AVAILABLE COPY U S DEPARTMENT EDUCATION OF HEALTH. NAT10N41
    [Show full text]
  • A Survey of Indian Logic from the Point of View of Computer Science
    Sadhana, "Col. 19, Part 6, December 1994, pp 971-983. © Printed in India A survey of Indian logic from the point of view of computer science V V S SARMA Department of Computer Science & Automation, Indian Institute of Science, Bangalore 560012, India Abstract. Indian logic has a long history. It somewhat covers the domains of two of the six schools (darsanas) of Indian philosophy, namely, Nyaya and Vaisesika. The generally accepted definition of In- dian logic over the ages is the science which ascertains valid knowledge either by means of six senses or by means of the five members of the syllogism. In other words, perception and inference constitute the sub- ject matter of logic. The science of logic evolved in India through three ~ges: the ancient, the medieval and the modern, spanning almost thirty centuries. Advances in Computer Science, in particular, in Artificial Intelligence have got researchers in these areas interested in the basic problems of language, logic and cognition in the past three decades. In the 1980s, Artificial Intelligence has evolved into knowledge-based and intelligent system design, and the knowledge base and inference engine have become standard subsystems of an intelligent System. One of the important issues in the design of such systems is knowledge acquisition from humans who are experts in a branch of learning (such as medicine or law) and transferring that knowledge to a computing system. The second important issue in such systems is the validation of the knowl- edge base of the system i.e. ensuring that the knowledge is complete and consistent.
    [Show full text]
  • The Etienne Gilson Series 21
    The Etienne Gilson Series 21 Remapping Scholasticism by MARCIA L. COLISH 3 March 2000 Pontifical Institute of Mediaeval Studies This lecture and its publication was made possible through the generous bequest of the late Charles J. Sullivan (1914-1999) Note: the author may be contacted at: Department of History Oberlin College Oberlin OH USA 44074 ISSN 0-708-319X ISBN 0-88844-721-3 © 2000 by Pontifical Institute of Mediaeval Studies 59 Queen’s Park Crescent East Toronto, Ontario, Canada M5S 2C4 Printed in Canada nce upon a time there were two competing story-lines for medieval intellectual history, each writing a major role for scholasticism into its script. Although these story-lines were O created independently and reflected different concerns, they sometimes overlapped and gave each other aid and comfort. Both exerted considerable influence on the way historians of medieval speculative thought conceptualized their subject in the first half of the twentieth cen- tury. Both versions of the map drawn by these two sets of cartographers illustrated what Wallace K. Ferguson later described as “the revolt of the medievalists.”1 One was confined largely to the academy and appealed to a wide variety of medievalists, while the other had a somewhat narrower draw and reflected political and confessional, as well as academic, concerns. The first was the anti-Burckhardtian effort to push Renaissance humanism, understood as combining a knowledge and love of the classics with “the discovery of the world and of man,” back into the Middle Ages. The second was inspired by the neo-Thomist revival launched by Pope Leo XIII, and was inhabited almost exclusively by Roman Catholic scholars.
    [Show full text]
  • Logical Empiricism / Positivism Some Empiricist Slogans
    4/13/16 Logical empiricism / positivism Some empiricist slogans o Hume’s 18th century book-burning passage Key elements of a logical positivist /empiricist conception of science o Comte’s mid-19th century rejection of n Motivations for post WW1 ‘scientific philosophy’ ‘speculation after first & final causes o viscerally opposed to speculation / mere metaphysics / idealism o Duhem’s late 19th/early 20th century slogan: o a normative demarcation project: to show why science ‘save the phenomena’ is and should be epistemically authoritative n Empiricist commitments o Hempel’s injunction against ‘detours n Logicism through the realm of unobservables’ Conflicts & Memories: The First World War Vienna Circle Maria Marchant o Debussy: Berceuse héroique, Élégie So - what was the motivation for this “revolutionary, written war-time Paris (1914), heralds the ominous bugle call of war uncompromising empricism”? (Godfrey Smith, Ch. 2) o Rachmaninov: Études-Tableaux Op. 39, No 8, 5 “some of the most impassioned, fervent work the composer wrote” Why the “massive intellectual housecleaning”? (Godfrey Smith) o Ireland: Rhapsody, London Nights, London Pieces a “turbulant, virtuosic work… Consider the context: World War I / the interwar period o Prokofiev: Visions Fugitives, Op. 22 written just before he fled as a fugitive himself to the US (1917); military aggression & sardonic irony o Ravel: Le Tombeau de Couperin each of six movements dedicated to a friend who died in the war x Key problem (1): logicism o Are there, in fact, “rules” governing inference
    [Show full text]
  • Mathematical Logic Part One
    Mathematical Logic Part One An Important Question How do we formalize the logic we've been using in our proofs? Where We're Going ● Propositional Logic (Today) ● Basic logical connectives. ● Truth tables. ● Logical equivalences. ● First-Order Logic (Today/Friday) ● Reasoning about properties of multiple objects. Propositional Logic A proposition is a statement that is, by itself, either true or false. Some Sample Propositions ● Puppies are cuter than kittens. ● Kittens are cuter than puppies. ● Usain Bolt can outrun everyone in this room. ● CS103 is useful for cocktail parties. ● This is the last entry on this list. More Propositions ● I came in like a wrecking ball. ● I am a champion. ● You're going to hear me roar. ● We all just entertainers. Things That Aren't Propositions CommandsCommands cannotcannot bebe truetrue oror false.false. Things That Aren't Propositions QuestionsQuestions cannotcannot bebe truetrue oror false.false. Things That Aren't Propositions TheThe firstfirst halfhalf isis aa validvalid proposition.proposition. I am the walrus, goo goo g'joob JibberishJibberish cannotcannot bebe truetrue oror false. false. Propositional Logic ● Propositional logic is a mathematical system for reasoning about propositions and how they relate to one another. ● Every statement in propositional logic consists of propositional variables combined via logical connectives. ● Each variable represents some proposition, such as “You liked it” or “You should have put a ring on it.” ● Connectives encode how propositions are related, such as “If you liked it, then you should have put a ring on it.” Propositional Variables ● Each proposition will be represented by a propositional variable. ● Propositional variables are usually represented as lower-case letters, such as p, q, r, s, etc.
    [Show full text]
  • Logic, Sets, and Proofs David A
    Logic, Sets, and Proofs David A. Cox and Catherine C. McGeoch Amherst College 1 Logic Logical Statements. A logical statement is a mathematical statement that is either true or false. Here we denote logical statements with capital letters A; B. Logical statements be combined to form new logical statements as follows: Name Notation Conjunction A and B Disjunction A or B Negation not A :A Implication A implies B if A, then B A ) B Equivalence A if and only if B A , B Here are some examples of conjunction, disjunction and negation: x > 1 and x < 3: This is true when x is in the open interval (1; 3). x > 1 or x < 3: This is true for all real numbers x. :(x > 1): This is the same as x ≤ 1. Here are two logical statements that are true: x > 4 ) x > 2. x2 = 1 , (x = 1 or x = −1). Note that \x = 1 or x = −1" is usually written x = ±1. Converses, Contrapositives, and Tautologies. We begin with converses and contrapositives: • The converse of \A implies B" is \B implies A". • The contrapositive of \A implies B" is \:B implies :A" Thus the statement \x > 4 ) x > 2" has: • Converse: x > 2 ) x > 4. • Contrapositive: x ≤ 2 ) x ≤ 4. 1 Some logical statements are guaranteed to always be true. These are tautologies. Here are two tautologies that involve converses and contrapositives: • (A if and only if B) , ((A implies B) and (B implies A)). In other words, A and B are equivalent exactly when both A ) B and its converse are true.
    [Show full text]
  • Peirce, Pragmatism, and the Right Way of Thinking
    SANDIA REPORT SAND2011-5583 Unlimited Release Printed August 2011 Peirce, Pragmatism, and The Right Way of Thinking Philip L. Campbell Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.. Approved for public release; further dissemination unlimited. Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily con- stitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy.
    [Show full text]
  • Lecture 1: Propositional Logic
    Lecture 1: Propositional Logic Syntax Semantics Truth tables Implications and Equivalences Valid and Invalid arguments Normal forms Davis-Putnam Algorithm 1 Atomic propositions and logical connectives An atomic proposition is a statement or assertion that must be true or false. Examples of atomic propositions are: “5 is a prime” and “program terminates”. Propositional formulas are constructed from atomic propositions by using logical connectives. Connectives false true not and or conditional (implies) biconditional (equivalent) A typical propositional formula is The truth value of a propositional formula can be calculated from the truth values of the atomic propositions it contains. 2 Well-formed propositional formulas The well-formed formulas of propositional logic are obtained by using the construction rules below: An atomic proposition is a well-formed formula. If is a well-formed formula, then so is . If and are well-formed formulas, then so are , , , and . If is a well-formed formula, then so is . Alternatively, can use Backus-Naur Form (BNF) : formula ::= Atomic Proposition formula formula formula formula formula formula formula formula formula formula 3 Truth functions The truth of a propositional formula is a function of the truth values of the atomic propositions it contains. A truth assignment is a mapping that associates a truth value with each of the atomic propositions . Let be a truth assignment for . If we identify with false and with true, we can easily determine the truth value of under . The other logical connectives can be handled in a similar manner. Truth functions are sometimes called Boolean functions. 4 Truth tables for basic logical connectives A truth table shows whether a propositional formula is true or false for each possible truth assignment.
    [Show full text]
  • Logic and Truth Tables Truth Tables Are Logical Devices That Predominantly Show up in Mathematics, Computer Science, and Philosophy Applications
    Logic and Truth Tables Truth tables are logical devices that predominantly show up in Mathematics, Computer Science, and Philosophy applications. They are used to determine the truth or falsity of propositional statements by listing all possible outcomes of the truth-values for the included propositions. Proposition - A sentence that makes a claim (can be an assertion or a denial) that may be either true or false. This is a Proposition – It is a complete sentence and Examples – “Roses are beautiful.” makes a claim. The claim may or may not be true. This is NOT a proposition – It is a question and does “Did you like the movie?” not assert or deny anything. Conjunction – an “and” statement. Given two propositions, p and q, “p and q” forms a conjunction. The conjunction “p and q” is only true if both p and q are true. The truth table can be set up as follows… This symbol can be used to represent “and”. Truth Table for Conjunction “p and q” (p ˄ q) p q p and q True True True True False False False True False False False False Examples – Determine whether the Conjunction is True or False. a. The capital of Ireland is Dublin and penguins live in Antarctica. This Conjunction is True because both of the individual propositions are true. b. A square is a quadrilateral and fish are reptiles. This Conjunction is False because the second proposition is false. Fish are not reptiles. 1 Disjunction – an “or” statement. Given two propositions, p and q, “p or q” forms a disjunction.
    [Show full text]
  • Passmore, J. (1967). Logical Positivism. in P. Edwards (Ed.). the Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan
    Passmore, J. (1967). Logical Positivism. In P. Edwards (Ed.). The Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan. LOGICAL POSITIVISM is the name given in 1931 by A. E. Blumberg and Herbert Feigl to a set of philosophical ideas put forward by the Vienna circle. Synonymous expressions include "consistent empiricism," "logical empiricism," "scientific empiricism," and "logical neo-positivism." The name logical positivism is often, but misleadingly, used more broadly to include the "analytical" or "ordinary language philosophies developed at Cambridge and Oxford. HISTORICAL BACKGROUND The logical positivists thought of themselves as continuing a nineteenth-century Viennese empirical tradition, closely linked with British empiricism and culminating in the antimetaphysical, scientifically oriented teaching of Ernst Mach. In 1907 the mathematician Hans Hahn, the economist Otto Neurath, and the physicist Philipp Frank, all of whom were later to be prominent members of the Vienna circle, came together as an informal group to discuss the philosophy of science. They hoped to give an account of science which would do justice -as, they thought, Mach did not- to the central importance of mathematics, logic, and theoretical physics, without abandoning Mach's general doctrine that science is, fundamentally, the description of experience. As a solution to their problems, they looked to the "new positivism" of Poincare; in attempting to reconcile Mach and Poincare; they anticipated the main themes of logical positivism. In 1922, at the instigation of members of the "Vienna group," Moritz Schlick was invited to Vienna as professor, like Mach before him (1895-1901), in the philosophy of the inductive sciences. Schlick had been trained as a scientist under Max Planck and had won a name for himself as an interpreter of Einstein's theory of relativity.
    [Show full text]