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Thanks to every one for the first lesson. I am glad to have such a lovely audience)

We`ve learned the folowing words:

Sentence, narrative, incentive, question, exclamation, expression, interpretation, variable, integer, real, relation, operator, value, equality, addition, plus, substraction, minus, multiplication, times, division, over, conjunction, and, disjuncton, or, negation, not, implication, if then, implies, equivalence, if and only if, brackets,conventional.
We have learned how to find out whether the narrative text is true or false, knowing truth values of the simple sentences.

Simple sentences are expressions, and the expressions are variables which can have two values: “0” or “1”.

Expressions can be connected in many ways. These ways called logical operators. They are: conjunction (and), disjuncton (or), negation (not), implication( if then), equivalence (if and only if). They are similar to *,+,1-x.

Brakets express logical emphasis from natural language in math and logic in the same way.

So you can:

text → {expressions, connections}→{variables, operators, brackets}→{formula}+ variable values → {truth value} → … → profit!
We have resolved some personal worth into exchange value tasks. Here they are:

  1. Turn to formula, decide truth values of the variables and evaluate.

    1. “If I go to the forest and meet a bear there, I will scare to death, forget about the meating with my friend. So, in order not to forget about the meating with my friend, i won`t go to the forest”

    2. “I play badminton. And it is not true that I play piano.”

  2. Find values of the variables to make the following expression a true one.

    1. “There are three students and some of them study logic. If the first one studies logic then the third one does . And it is not true that if the third one does then the second one studies as well.”
  3. Make a schedule on three periods with three subjects for three teachers taking into accout their wishes (time when they want to come).

We have encountered some problems

  1. “or” sometimes means “xor” in a natural language

  2. Bear not ( not ( g and b ) or ( s and f ) ) or ( not not f or not g )

  3. implication has contraintuitive truth table

  4. in construction “. However, it is not true that...” one can think that “it” referes to .

  5. In task “there are three students and some of them study logic” we got two answers instead one. Why?

  6. In schedule making we had some proposals which didn`t work. There are three conditions to be held.

    1. All subjects must take place.

    2. Each subject must take place once.

    3. Consern teachers` requirenments. Eg the mathematician says: “I can come either on the first period or in the third one”.

Small but incorrect formula. What`s the idea? Where is the mistake? (Pavlo)

not G1 and not P2 and not M3 and ((M1 and not P1) or (not M1 and not P1)) and (( M2 and not G2) or (not M2 and G2)) and ((P3 and not G3) or (not P3 and G3)
Vadim’s proposal

((M1 or M2) and not M3)… for each teacher.

((M1 or m2) and not M3) and ((P1 or P3) and not P2) and ((G2 or G3) and not G1)

( ( ( m1 and not m2 ) or ( not m1 and m2 ) ) and not m3 ) and ( ( ( p1 and not p3 ) or ( not p1 and p3 ) ) and not p2 ) and ( ( ( g2 and not g3 ) or ( not g2 and g3 ) ) and not g1 )

Vadim’s question: “Does it matter whether to go through rows or colums? (in schedule making)”

Big formula for schelule:

(M1 or M2 or M3) and (P1 or P2 or P3) and (G1 or G2 or G3) and

not (M1 and M2) and not (M1 and M3) and not (M2 and M3) and

not (P1 and P2) and not (P1 and P3) and not (P2 and P3) and

not (G1 and G2) and not (G1 and G3) and not (G2 and G3) and

not G1 and not P2 and not M3

Does it work?

Here are some tasks you may want to do.
Decide who from four students has passed the exam provided you know:

If the first one has passed then the second one has passed.

If the second one has passed then the third one did or the first one has not.

If the fourth one hasn`t passed then the first one has passed and the third one hasn`t.

If the fourth one has passed then the first one has.
Roksa, Dafna and Gudya have found an ancient zayavka. Having looked at a wonderful item they have made the following conclusions:

Roksa: This item is Greek and was made in the V century.

Dafna: This item is Finikian and was made in the III century.

Gudya: This item is not Greek and it was made in the IV century.

Yasha told fellows that each of them was right only in one of their conclusions.

Where and when was the item made.
Here are some future topics:

  • law and logic. Formalization of laws. (need assistance)

  • mathematical proof. True proof of some school theorems. Not just learning by hart. (logic of predicates needed)

  • electric schemes as in school physics. From a logical formula. (ready)

  • functional schemes as in computer processor architecture. From a logical formula. (ready)

  • logical fundamentals of English syntax (idea)

  • Logics & semiotics (they are related, aren`t they?)

  • Simplification of the narrative text (ready). Contrary to the student reality, making a small text out of big one:)

  • Relations and Predicates. Predicates are expressions where the subject is a variable. (ready)

  • Logic in philosophy (need assistance).

  • Set theory. All infinities are infinite, but some of them infinite even more (ready)

  • Godel theorem (not ready)

  • Finding optimal trips for pedestrian (ready to start)