1 Initial Ideas on Formal Methodsuit2206/slides/slides_01.color.pdf · 1—Initial Ideas on Formal Methods UIT2206: The Importance of Being Formal Martin Henz January 15, 2014 Generated

PreliminariesHallmarks of a Formal Approach

Formal Systems in Information Technology

1—Initial Ideas on Formal Methods

UIT2206: The Importance of Being Formal

Martin Henz

January 15, 2014

Generated on Wednesday 15th January, 2014, 09:54

UIT2206: The Importance of Being Formal 1—Initial Ideas on Formal Methods



1 Preliminaries

2 Hallmarks of a Formal Approach

3 Formal Systems in Information Technology




Structure of the module

Intro (today)Formal reasoning techniques (Weeks 2 to 8)Formal methods in other disciplines (Weeks 9 to 12)




Weekly structure

Lecture: Wednesdays 10–12Tutorials: two sessions on Fridays: 8–10 and 10–12starting next week




Assessment

Class participation: 10%Tutorial participation: 10%Assignments: 20%Test (Week 9 or 10): 20%Presentation (Weeks 10 to 13): 20%Essay: 20%




DiscretenessNamingAbstractionReificationSelf-reference

1 Preliminaries

2 Hallmarks of a Formal ApproachDiscretenessNamingAbstractionReificationSelf-reference

3 Formal Systems in Information Technology





Discreteness

Do atoms exist?

Brownian motion

Fundamental factNature is made up of discrete structures

Central dogma of molecular biologyDNA makes RNA makes protein


http://en.wikipedia.org/wiki/Brownian_motion




Discreteness

Do atoms exist?Brownian motion








Discreteness









Discreteness



Central dogma of molecular biology

DNA makes RNA makes protein






Discreteness









Discreteness in Human Affairs

LanguageNatural language is made up of sounds, words, sentences. Allof these are discrete structures

PoliticsStates, counties, political parties etc are discrete, notcontinuous phenomena





Discreteness in Human Affairs

LanguageNatural language is made up of sounds, words, sentences. Allof these are discrete structures

PoliticsStates, counties, political parties etc are discrete, notcontinuous phenomena





Naming

John Stuart MillsNames have denotations, not connotations

Frege/RussellNames are essentially abbreviations for a collection ofproperties

A Theory of NamingNaming is a surprisingly poorly understood concept. 20thcentury philosophers have made significant progress. Example:Saul Kripke: Naming and Necessity





Naming








Naming








Abstraction

DefinitionAbstraction is a process by which concepts are derived fromthe usage and classification of other (more “real” or “concrete”)concepts.

ScienceClassification of phenomena into discrete categories lies at theheart of many sciences. Example: taxonomy in biology





Abstraction

DefinitionAbstraction is a process by which concepts are derived fromthe usage and classification of other (more “real” or “concrete”)concepts.

ScienceClassification of phenomena into discrete categories lies at theheart of many sciences. Example: taxonomy in biology





Reification

DefinitionReification refers to making something real, bringing it intobeing, or making something concrete.

Automated processingReification is a prerequisite for automated processing





Reification

DefinitionReification refers to making something real, bringing it intobeing, or making something concrete.

Automated processingReification is a prerequisite for automated processing





Self-reference

Grelling-Nelson paradoxIs “non-self-descriptive” non-self-descriptive or self-descriptive?

ApplicationsSometimes, self-reference has surprising results: Godel’sTheorems, the Halting Problem





Self-reference







Self-reference






Formal Systems: A Standard Response to ComplexityFormal Systems All Around Us

1 Preliminaries

2 Hallmarks of a Formal Approach

3 Formal Systems in Information TechnologyFormal Systems: A Standard Response to ComplexityFormal Systems All Around Us





Example 1: Books

ProblemHow to identify a book uniquely, and world-wide

Attempts“Library of Congress”, need of fast access to records led toalternatives (publishers J Whitaker & Sons, R R Bowker)

SolutionISBN: 13-digit International Standard Book Number (ISOstandard), see example


http://en.wikipedia.org/wiki/International_Standard_Book_Number

http://en.wikipedia.org/wiki/International_Organization_for_Standardization

http://upload.wikimedia.org/wikipedia/commons/2/28/EAN-13-ISBN-13.svg




Example 1: Books











Example 1: Books











Example 2: Representing Text

ProblemHow to store and transmit text, given that dozens of scriptsexists, and hundreds of languages use them.

AttemptsASCII (95 characters), ISO 8859 (one “byte”)

SolutionUnicode standardizes more than 109,000 characters, covering93 scripts, developed by the Unicode Consortium


http://en.wikipedia.org/wiki/ASCII

http://en.wikipedia.org/wiki/ISO_8859

http://en.wikipedia.org/wiki/Unicode

http://en.wikipedia.org/wiki/Unicode_Consortium




























Example 3: Text Processing

ProblemIn the 1960s, some projects required amounts of documentsthat exceeded the processing capabilities of traditionaladministrative procedures.

AttemptsGML by IBM: named after inventors Goldfarb, Mosher, Lorie

Solution: SGML“SGML was...designed to enable the sharing ofmachine-readable large-project documents in government, law,and industry. Many such documents must remain readable forseveral decades—a long time in the information technologyfield.”


http://en.wikipedia.org/wiki/Standard_Generalized_Markup_Language






















Example 4: Hypertext

ProblemIn the late 1980s, it became clear that the Internet could beused to link documents together. For that, software needed torun on the client (browsers), and (web) servers.

Problem: How to make sure client software understands whatthe server is serving?

SolutionHTML, and application of SGML


http://en.wikipedia.org/wiki/HTML





ProblemIn the late 1980s, it became clear that the Internet could beused to link documents together. For that, software needed torun on the client (browsers), and (web) servers.Problem: How to make sure client software understands whatthe server is serving?








ProblemIn the late 1980s, it became clear that the Internet could beused to link documents together. For that, software needed torun on the client (browsers), and (web) servers.Problem: How to make sure client software understands whatthe server is serving?







Surprised?

Why do we not realize...

... that we are surrounded by formal systems?

Because they work!We do not need to know that what underlies complex systemsis a formal process. The formal systems allow them to work asexpected, always!





Surprised?

Why do we not realize...... that we are surrounded by formal systems?






Surprised?


Because they work!

We do not need to know that what underlies complex systemsis a formal process. The formal systems allow them to work asexpected, always!





Surprised?







The Importance of Being Formal

First AgendaFind out in detail how formal systems work

GoalThorough understanding of formal logic as an example parexcellence for formal methods

ApproachStudy a series of logics: traditional, propositional, predicatelogic






















Second AgendaExplore fundamental boundaries of formal reasoning

GoalAppreciate Undecidability and Godel’s incompleteness results

ApproachStudy predicate logic deep enough to understand his formalarguments






















Third AgendaExplore formal methods across fields

ApproachStudents write essays and present their findings

GoalOverview of formal methods and their limitations in ourcivilization


















Documents

1 Initial Ideas on Formal Methodsuit2206/slides/slides_01.color.pdf · 1—Initial Ideas on Formal Methods UIT2206: The Importance of Being Formal Martin Henz January 15, 2014 Generated