CIS 301. Declarative sentences.

Declarative sentences. A declarative sentence is a sentence, written in some language, that, if compared to our external or internal worlds, is either true or false. Examples of declarative sentences are:

(1). The sum of the numbers 3 and 5 equals 8.

(2). Jane reacted violently to Jack's accusations.

(3). Every even natural number is the sum of two prime numbers.

(4). All Martians like pepperoni on their pizza.

(5). Albert Camus etait un ecrivain francais.

(6). Die W"urde des Menschen ist unantastbar.

(7). No shoes, no shirt, no service.

Sentence (3) above is interesting. Although nobody apparantly knows, whether it is true, we can argue that is definitely is true or false. There is no third possibility. As the Romans said: tertium non datur. This seems trivial, but is a powerful principle that one has to abandon if truth is "replaced" with a computational witness of truth.

Examples of sentences that are not declarative are:

1. questions, e.g. "Could you please pass me the salt?",

2. commands, e.g. "Ready, steady, go!", or

3. wishes, e.g. "May fortune come your way."

Arguments:

Consider the following example of an argument:

If the train arrives late and there are no taxis at the station, then John is late for his meeting.
John is not late for his meeting.
The train did arrive late.
Therefore, there were taxis at the station.

Arguments are based on

a finite set of premises, what you assume as being true. For example, a premise for a presidential campaign could be "Our government has balanced the budget."
a conclusion, e.g. "Therefore I ask the American people to vote for ... as the next president of the United States of America."
and a systematic way of taken the given premises to "arrive" at the given conclusion. This process is usually called reasoning.

In Chapter 1, we learn how to do this. You may wonder why this seems much harder to apply in politics or general societal processes. For such complex issues it is often up to debate whether premises are actually true. And, unfortunately, politicians occasionally use a way of reasoning that is unsound. Luckily, these problems pretty much disappear when we apply reasoning toward computer systems!

Michael Huth (huth@cis.ksu.edu)