I signed up for a class that I shouldn't have. So now I'm slightly screwed because I don't understand any of the notation used when my professor was explaining first order logic. I need some book suggestions as to how to re-learn all of these things. For example: I was confused as to what a "quantifier" is (I do know after Googling it). Any good books with plenty of examples? Thanks
The logicians at UCLA have a free logic book covering first-order logic here.
One of the nice things about the book is that it's written to be used in conjunction with a free software program to help learn logic.
I've taught three university logic courses and found the majority of students do much better by completing proofs and derivations in addition to reading about them. That said, if you approach learning logic in the same way as learning mathematics or programming you'll increase your chances for success.
Jon Barwise & John Etchemendy, The Language of First-Order Logic (CSLI Press, 1992) is great. A revised and expanded edition was released in 2002, titled Language, Proof and Logic.
Related
Learning Clips, while I don't mind the syntax I'm finding it difficult to derive rules from facts. Is there a tip on how to structure rules given a knowledge base?
A non trivial example would be nice, thanks.
Basically this is the entire field of "knowledge engineering;" it's really as broad a question as "given a domain, how do I architect application software for that domain?" Whole books have been written on this topic. Here are three that treat this topic well IMO: Peter Norvig's "Artificial Intelligence, A Modern Approach", Giarratano and Riley's "Expert Systems: Principles and Programming", and my "Jess In Action".
Currently in my comp., there are some changes going on regarding project documentation. There is a LOT of time and effort spent on discussing functional specs vs. requirements doc. However, I don't think anyone here understands the reason why you would use one over the other. Therefore, I don't understand the difference myself.
Can someone shed some light on this matter please? If you have links to articles, blog posts, etc. That would be helpful too.
A Requirements document should specify the requirements from the perspective of the end user.
User requirements document - Wikipedia
A Functional spec is a level lower and starts to define how different parts of the system should function at the System Engineering level:
Functional specification - Wikipedia
Requirements : “what” the application should do [from user's perspective view]
Functional specification: “how” the application function
Technical specification: “how” the function implemented
Requirement:
You must be in Edinburgh by 2pm tomorrow.
Specification:
Travel by car to the airport ... then take a connecting flight to .... then take the tram to the city centre ... then walk to ....
In general it's 'What's the outcome?' versus 'How are we going to do it?'.
Business Requirement:
Implement a computerized system that calculating employees wages with required deductions and additions and pay the amount the employee is actually owed.
Functional Requirements
How many employees in the company and their details
Are they part-time, or full-time or hourly
What is the pay date
What is the deductions like TAX, PF, Community Contributions etc
I was enjoying "The Humble Programmer" earlier today and ran across this choice quote:
Therefore, for the time being and perhaps forever, the rules of the second kind present themselves as elements of discipline required from the programmer. Some of the rules I have in mind are so clear that they can be taught and that there never needs to be an argument as to whether a given program violates them or not. Examples are the requirements that no loop should be written down without providing a proof for termination nor without stating the relation whose invariance will not be destroyed by the execution of the repeatable statement.
I'm looking for which of Dijkstra's 1300+ writings best describe in further detail rules such as he was describing above.
Page 5 through 18: http://userweb.cs.utexas.edu/users/EWD/ewd02xx/EWD249.PDF
Mid. page 3 through end: http://userweb.cs.utexas.edu/users/EWD/ewd04xx/EWD473.PDF
End page 5 through end: http://userweb.cs.utexas.edu/users/EWD/ewd06xx/EWD641.PDF
All: http://userweb.cs.utexas.edu/users/EWD/transcriptions/EWD02xx/EWD261.html (Dutch, translation=below)
Note: Dijkstra numbers his pages starting at 0. Given page numbers are starting at 1, the PDF page number, and not the written page numbers.
My translation of EWD261 in English:
How to program mathematically
A (well-defined) programme is structured just like a (well-defined) mathematical theory. The programmers' work is not different from that of a creative mathematician.
There are small, but important, differences, though:
There are not much basic concepts of programming and they are not difficult to comprehend (though misleadingly simple); this is why it's an ideal for development practice. (Besides this, there is the fact that a demand for correctness, the programme should really work!)
With most mathematical education one learns about existing theorems, viz. equipping a student with a specific (detailed) set of concepts; a programmer, however, has to develop the needed concept himself. Programming requires the abstractions which leads to a type of creativity, while the same in mathematics is limited to applying existing theorems.
Because programmes are big and nevertheless have to work will programmers learn how to develop carefully and consciously. This is exactly what one should teach! To teach extensive knowledge is, for me, not justified.
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Inspired after watching Michael Feather's SCNA talk "Self-Education and the Craftsman", I am interested to hear about practical examples in software development where discrete mathematics have proved helpful.
Discrete math has touched every aspect of software development, as software development is based on computer science at its core.
http://en.wikipedia.org/wiki/Discrete_math
Read that link. You will see that there are numerous practical applications, although this wikipedia entry speaks mainly in theoretical terms.
Techniques I learned in my discrete math course from university helped me quite a bit with the Professor Layton games.
That counts as helpful... right?
There are a lot of real-life examples where map coloring algorithms are helpful, besides just for coloring maps. The question on my final exam had to do with traffic light programming on a six-way intersection.
As San Jacinto indicates, the fundamentals of programming are very much bound up in discrete mathematics. Moreover, 'discrete mathematics' is a very broad term. These things perhaps make it harder to pick out particular examples. I can come up with a handful, but there are many, many others.
Compiler implementation is a good source of examples: obviously there's automata / formal language theory in there; register allocation can be expressed in terms of graph colouring; the classic data flow analyses used in optimizing compilers can be expressed in terms of functions on lattice-like algebraic structures.
A simple example the use of directed graphs is in a build system that takes the dependencies involved in individual tasks by performing a topological sort. I suspect that if you tried to solve this problem without having the concept of a directed graph then you'd probably end up trying to track the dependencies all the way through the build with fiddly book-keeping code (and then finding that your handling of cyclic dependencies was less than elegant).
Clearly most programmers don't write their own optimizing compilers or build systems, so I'll pick an example from my own experience. There is a company that provides road data for satnav systems. They wanted automatic integrity checks on their data, one of which was that the network should all be connected up, i.e. it should be possible to get to anywhere from any starting point. Checking the data by trying to find routes between all pairs of positions would be impractical. However, it is possible to derive a directed graph from the road network data (in such a way as it encodes stuff like turning restrictions, etc) such that the problem is reduced to finding the strongly connected components of the graph - a standard graph-theoretic concept which is solved by an efficient algorithm.
I've been taking a course on software testing, and 3 of the lectures were dedicated to reviewing discrete mathematics, in relation to testing. Thinking about test plans in those terms seems to really help make testing more effective.
Understanding of set theory in particular is especially important for database development.
I'm sure there are numerous other applications, but those are two that come to mind here.
Just example of one of many many...
In build systems it's popular to use topological sorting of jobs to do.
By build system I mean any system where we have to manage jobs with dependency relation.
It can be compiling program, generating document, building building, organizing conference - so there is application in task management tools, collaboration tools etc.
I believe testing itself properly procedes from modus tollens, a concept of propositional logic (and hence discrete math), modus tollens being:
P=>Q. !Q, therefore !P.
If you plug in "If the feature is working properly, the test will pass" for P=>Q, and then take !Q as given ("the test did not pass"), then, if all these statements are factually correct, you have a valid, sound basis for returning the feature for a fix. By contrast, many, maybe most testers operate by the principle:
"If the program is working properly, the test will pass. The test passed, therefore the program is working properly."
This can be written as: P=>Q. Q, therefore P.
But this is the fallacy of "affirming the consequent" and does not show what the tester believes it shows. That is, they mistakenly believe that the feature has been "validated" and can be shipped. When Q is given, P may in fact either be true or it may be untrue for P=>Q, and this can be shown with a truth table.
Modus tollens is core to Karl Popper's notion of science as falsification, and testing should proceed in much the same way. We're attempting to falsify the claim that the feature always works under every explicit and implicit circumstance, rather than attempting to verify that it works in the narrow sense that it can work in some proscribed way.
An initial draft of requirements specification has been completed and now it is time to take stock of requirements, review the specification. Part of this process is to make sure that there are no sizeable gaps in the specification. Needless to say that the gaps lead to highly inaccurate estimates, inevitable scope creep later in the project and ultimately to a death march.
What are the good, efficient techniques for pinpointing missing and implicit requirements?
This question is about practical techiniques, not general advice, principles or guidelines.
Missing requirements is anything crucial for completeness of the product or service but not thought of or forgotten about,
Implicit requirements are something that users or customers naturally assume is going to be a standard part of the software without having to be explicitly asked for.
I am happy to re-visit accepted answer, as long as someone submits better, more comprehensive solution.
Continued, frequent, frank, and two-way communication with the customer strikes me as the main 'technique' as far as I'm concerned.
It depends.
It depends on whether you're being paid to deliver what you said you'd deliver or to deliver high quality software to the client.
If the former, simply eliminate ambiguity from the specifications and then build what you agreed to. Try to stay away from anything not measurable (like "fast", "cool", "snappy", etc...).
If the latter, what Galwegian said + time or simply cut everything not absolutely drop-dead critical and build that as quickly as you can. Production has a remarkable way of illuminating what you missed in Analysis.
evaluate the lifecycle of the elements of the model with respect to a generic/overall model such as
acquisition --> stewardship --> disposal
do you know where every entity comes from and how you're going to get it into your system?
do you know where every entity, once acquired, will reside, and for how long?
do you know what to do with each entity when it is no longer needed?
for a more fine-grained analysis of the lifecycle of the entities in the spec, make a CRUDE matrix for the major entities in the requirements; this is a matrix with the operations/applications as the rows and the entities as the columns. In each cell, put a C if the application Creates the entity, R for Reads, U for Updates, D for Deletes, or E for "Edits"; 'E' encompasses C,R,U, and D (most 'master table maintenance' apps will be Es). Then check each column for C,R,U, and D (or E); if one is missing (except E), figure out if it is needed. The rows and columns of the matrix can be rearranged (manually or using affinity analysis) to form cohesive groups of entities and applications which generally correspond to subsystems; this may assist with physical system distribution later.
It is also useful to add a "User" entity column to the CRUDE matrix and specify for each application (or feature or functional area or whatever you want to call the processing/behavioral aspects of the requirements) whether it takes Input from the user, produces Output for the user, or Interacts with the user (I use I, O, and N for this, and always make the User the first column). This helps identify where user-interfaces for data-entry and reports will be required.
the goal is to check the completeness of the specification; the techniques above are useful to check to see if the life-cycle of the entities are 'closed' with respect to the entities and applications identified
Here's how you find the missing requirements.
Break the requirements down into tiny little increments. Really small. Something that can be built in two weeks or less. You'll find a lot of gaps.
Prioritize those into what would be best to have first, what's next down to what doesn't really matter very much. You'll find that some of the gap-fillers didn't matter. You'll also find that some of the original "requirements" are merely desirable.
Debate the differences of opinion as to what's most important to the end users and why. Two users will have three opinions. You'll find that some users have no clue, and none of their "requirements" are required. You'll find that some people have no spine, and things they aren't brave enough to say out loud are "required".
Get a consensus on the top two or three only. Don't argue out every nuance. It isn't possible to envision software. It isn't possible for anyone to envision what software will be like and how they will use it. Most people's "requirements" are descriptions of how the struggle to work around the inadequate business processes they're stuck with today.
Build the highest-priority, most important part first. Give it to users.
GOTO 1 and repeat the process.
"Wait," you say, "What about the overall budget?" What about it? You can never know the overall budget. Do the following.
Look at each increment defined in step 1. Provide a price-per-increment. In priority order. That way someone can pick as much or as little as they want. There's no large, scary "Big Budgetary Estimate With A Lot Of Zeroes". It's all negotiable.
I have been using a modeling methodology called Behavior Engineering (bE) that uses the original specification text to create the resulting model when you have the model it is easier to identify missing or incomplete sections of the requirements.
I have used the methodolgy on about six projects so far ranging from less than a houndred requirements to over 1300 requirements. If you want to know more I would suggest going to www.behaviorengineering.org there some really good papers regarding the methodology.
The company I work for has created a tool to perform the modeling. The work rate to actually create the model is about 5 requirements for a novice and an expert about 13 requirements an hour. The cool thing about the methodolgy is you don't need to know really anything about the domain the specification is written for. Using just the user text such as nouns and verbs the modeller will find gaps in the model in a very short period of time.
I hope this helps
Michael Larsen
How about building a prototype?
While reading tons of literature about software requirements, I found these two interesting books:
Problem Frames: Analysing & Structuring Software Development Problems by Michael Jackson (not a singer! :-).
Practical Software Requirements: A Manual of Content and Style by Bendjamen Kovitz.
These two authors really stand out from the crowd because, in my humble opinion, they are making a really good attempt to turn development of requirements into a very systematic process - more like engineering than art or black magic. In particular, Michael Jackson's definition of what requirements really are - I think it is the cleanest and most precise that I've ever seen.
I wouldn't do a good service to these authors trying to describe their aproach in a short posting here. So I am not going to do that. But I will try to explain, why their approach seems to be extremely relevant to your question: it allows you to boil down most (not all, but most!) of you requirements development work to processing a bunch of check-lists* telling you what requirements you have to define to cover all important aspects of the entire customer's problem. In other words, this approach is supposed to minimize the risk of missing important requirements (including those that often remain implicit).
I know it may sound like magic, but it isn't. It still takes a substantial mental effort to come to those "magic" check-lists: you have to articulate the customer's problem first, then analyze it thoroughly, and finally dissect it into so-called "problem frames" (which come with those magic check-lists only when they closely match a few typical problem frames defined by authors). Like I said, this approach does not promise to make everything simple. But it definitely promises to make requirements development process as systematic as possible.
If requirements development in your current project is already quite far from the very beginning, it may not be feasible to try to apply the Problem Frames Approach at this point (although it greatly depends on how your current requirements are organized). Still, I highly recommend to read those two books - they contain a lot of wisdom that you may still be able to apply to the current project.
My last important notes about these books:
As far as I understand, Mr. Jackson is the original author of the idea of "problem frames". His book is quite academic and theoretical, but it is very, very readable and even entertaining.
Mr. Kovitz' book tries to demonstrate how Mr. Jackson ideas can be applied in real practice. It also contains tons of useful information on writing and organizing the actual requirements and requirements documents.
You can probably start from the Kovitz' book (and refer to Mr. Jackson's book only if you really need to dig deeper on the theoretical side). But I am sure that, at the end of the day, you should read both books, and you won't regret that. :-)
HTH...
I agree with Galwegian. The technique described is far more efficient than the "wait for customer to yell at us" approach.