computer science

Language, Proof and Logic

Language, Proof and Logic is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Language, Proof and Logic rather than just read about it. In short: Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic through the use of a tight integration between a textbook (same name as the package) and four software programs, where three of them are logic related (Boole, Fitch and Tarski's World) and the other (Submit) is an internet-based grading service. The name is a pun deriv…

Key takeaways

Language, Proof and Logic belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Language, Proof and Logic to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Language, Proof and Logic from memory before moving on to harder problems.

Reference excerpt

Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic through the use of a tight integration between a textbook (same name as the package) and four software programs, where three of them are logic related (Boole, Fitch and Tarski's World) and the other (Submit) is an internet-based grading service. The name is a pun derived from Language, Truth, and Logic, the philosophy book by A. J. Ayer. On September 2, 2014, there was launched a massive open online course (MOOC) with the same name, which utilizes this educational software package.

Description A short description of the programs:

Boole (named after George Boole) - a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.); Fitch (named after Frederic Brenton Fitch) - a natural deduction proof environment in Fitch-style calculus for giving and checking first-order proofs; Tarski's World (named after Alfred Tarski) - a program that teaches the basic first-order language and its semantics using a model theoretic-like approach, where the "world" consists of a little grid and some simple objects; Submit - a program that allows students to submit exercises done with the above programs to the Grade Grinder, the online grading service.

References

External links Home page 1st edition of Language, Proof and Logic at Internet Archive massive open online course (MOOC) of Language, Proof and Logic

Worked examples

Example 1 — a first encounter with Language, Proof and Logic

Start with the simplest possible case. Write down what Language, Proof and Logic claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Language, Proof and Logic before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Language, Proof and Logic ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Language, Proof and Logic

In research: Language, Proof and Logic appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Language, Proof and Logic in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Language, Proof and Logic is common in secondary-school and first-year university syllabi. It links to neighbouring topics Digital media works about philosophy, Educational software, Logic, so understanding it makes those chapters shorter.
In everyday life: Look for Language, Proof and Logic outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Language, Proof and Logic in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Language, Proof and Logic means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Language, Proof and Logic out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Language, Proof and Logic in simple terms?

Why does Language, Proof and Logic matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Language, Proof and Logic?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Language, Proof and Logic.