Example of variables and quantifiers - first-order logic, Computer Engineering

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Example of Variables and quantifiers:

We should have started with something such
2207_Example of Variables and quantifiers.png

which reflects the fact that we're really talking for some meal at the Red Lion, nevertheless than a particular one. Moreover, this isn't relatively specific enough. Actually we use to tell the reader of our translated sentence something more for our beliefs concerning the variable X. Such in this case, we require to tell the reader that we believe there exists like an X. So then there is a specific symbol in predicate logic which we use for this purpose, calling the 'exists symbol'. And this is written in also: . In fact we put it around our pair of predicates, whenever we get a fully formed sentence in first-order logic:

As above we seen this is read as "there is something calling X, here X is a meal and X costs three pounds at the Red Lion".
For now if we want to say that all meals at the Red Lion cost three pounds. So than in this such case, we use to different symbol, that we call the 'forall' symbol. According to that this states that the predicates concerning the variable to that the symbol applies are true to all possible instances of variable. Nevertheless, what would come to pass if we replaced the exists symbol more than by our new forall symbol?? We would catch this:

2207_Example of Variables and quantifiers.png

If is this actually that we wanted to already say? Aren't we saying something on the subject of all meals in the universe? So well, in reality we're saying something about every item in the Universe: the whole lot is a meal which you can buy from the Red Lion. Just for three pounds! What we in actuality wanted to say should have been expressed more such of represent as this:

1247_Example of Variables and quantifiers1.png

Well this is read as: for all objects or items X, if X is a meal, so it costs three pounds in the Red Lion. If we're still not there than though. Exactly this implies that every meal can be brought at the Red Lion. There is possibly we should throw in another predicate: serves like Pub, Meal that states such as Pub serves the Meal. Now what we wanted to say we can finally write:

303_Example of Variables and quantifiers2.png

This can be read as: for all objects X, if X is a meal and X is served in the Red Lion, then X costs three pounds.


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