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Logic provides a way to talk about truth and correctness in a rigourous way,so that we can prove things, rather than make intelligent guesses and just hope they are correct.

The ancient Greeks loved to hang around on the stoa , sip some wine, and debate.But at the end of the day, they wanted to sit back and decide who had won the argument.When Socrates claims that one statement follows from another, is it actually so?Shouldn't there be some set of rules to officially determine when an argument is correct?Thus began the formal study of logic.

The three fundamental studies were the Trivium grammar (words), logic (reasoning), and rhetoric (effective communication).These allowed study of the Quadrivium arithmetic (patterns in number),geometry (patterns in space), music (patterns in tone), andastronomy (patterns in time). All together, these subjects comprise the seven liberal arts .

These issues are of course still with us today. And while it might be difficult to codify real-worldarguments about (say) gun-control laws, programs can be fully formalized, and correctness can be specified.We'll look at three examples where formal proofs are applicable:

  • playing a simple game, WaterWorld;
  • checking a program for type errors;
  • circuit verification.
Many other areas of computer science routinely involve proofs, although we won't explore them here.Manufacturing robots first prove that they can twist and move to where they need to go before doing so, in order to avoid crashing intowhat they're building. When programming a collection of client and server computers,we usually want to prove that the manner in which they communicate guarantees that no clients are always ignored.Optimizing compilers prove that, within your program, some faster piece of code behaves the same as and can replace what you wrote.With software systems controlling more and more life-critical applications, it's important to be able to prove that a program always does what it claims.

Waterworld

Consider a game called WaterWorld, where each location is either empty sea or contains a pirate.When you enter a location, you must correctly anticipate whether or not it contains pirates.

  • If you correctly anticipate open sea, you are able to enter and determine how many of the (up to 3) adjacent locations containa pirate.
  • If you correctly anticipate a pirate, the location is tagged as dangerous, and you gather no further information.
Furthermore, there are really two types of moves: guesses, and assertions.If you make an assertion, then even if you happen to be correct but it is possible you could have been wrong, then it is an error.Also, it is an error if you make a guess about a location if it is actually possible to assert a location's contents.The interesting fact about these types of games is that while sometimes guesses are necessary (when?),surprisingly often an assertion can be made.

(You can freely download WaterWorld .)

Glimpses of two different WaterWorld boards

Questions & Answers

I'm interested in biological psychology and cognitive psychology
Tanya Reply
what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
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ARC
A child is a member of community not society elucidate ?
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Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
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explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
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Jonathan
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Jonathan
generally amnesi how long yrs memory loss
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interpersonal relationships
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What would be the best educational aid(s) for gifted kids/savants?
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Source:  OpenStax, Intro to logic. OpenStax CNX. Jan 29, 2008 Download for free at http://cnx.org/content/col10154/1.20
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