## From English to Proposition

### Subjects to be Learned

- translation of English sentences to propositions

### Contents

As we are going to see in the next section, reasoning is done on propositions
using inference rules. For example, if the two propositions "if it snows,
then the school is closed",
and "it snows" are true, then we can conclude that "the school is closed" is true.
In everyday life, that is how we reason.

To check the correctness of reasoning, we must check whether or not rules of
inference have been followed to draw the conclusion from the premises.
However, for reasoning in English or
in general for reasoning in a natural language, that is not necessarily straightforward and
it often encounters some difficulties. Firstly,
connectives are not necessarily easily identified as we can get a flavor of that
from the previous topic on variations of if_then statements. Secondly, if the
argument becomes complicated involving many statements in a number of different
forms twisted and tangled up, it can easily get out of hand unless it is simplified in some way.

One solution for that is to use symbols (and mechanize it). Each sentence is represented by symbols
representing building block sentences, and connectives. For example, if
*P* represents "it snows" and *Q* represents "the school is
closed", then the previous argument can be expressed as

**[ [ ***P* -> *Q* ] **^** *P* ] -> *Q* ,

**or**

*P* -> *Q*

*P*

**
-----------------------------
**

** ***Q*

This representation is concise, much simpler and much easier to deal with.
In addition today there are a number of
automatic reasoning systems
and we can verify our arguments in symbolic form using them. One such system called TPS
is used for reasoning exercises in this course. For example, we can
**check the correctness** of our argument
using it.

**To convert English statements into a symbolic form**, we **restate the given statements
using the building block sentences, those for which symbols are given,
and the connectives of propositional logic**
(**not, and, or, if_then, if_and_only_if**), and **then substitute the symbols
for the building blocks and the connectives**.

**For example**, let *P* be the proposition "It is snowing",
*Q* be the proposition "I will go the beach",
and *R* be the proposition "I have time".

Then first "I will go to the beach if it is not snowing" is restated as
"If it is not snowing, I will go to the beach". Then symbols *P* and
*Q* are substituted for the respective sentences to obtain
**~***P* -> *Q*.

Similarly, "It is not snowing and I have time only if I will go to the beach" is restated as
"If it is not snowing and I have time, then I will go to the beach", and it is
translated as **( ~***P* ^ *R* ) -> *Q*.

### Test Your Understanding of English to Logic Translation

**Click Correct or Incorrect , then Submit. There is one set of questions.**

Note below **V** is used for "OR".

**
Next -- Reasoning with Propositions**

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