Take some carbon compounds naphthalene,camphor, alcohol one by one on a spatula and burn them. Observe the nature of the flame and note whether smoke is produced. Saturated hydrocarbons burn generally with clear blue flame in sufficient supply of air with no visible smoke Question 2. Place a metal plate above the flame.
The capital of Freedonia has a population of 9, No city in Freedonia has a population of 9, Freedonia is to the north of Sylvania. We have chosen sentences about fictional countries featured in the Marx Brothers' movie Duck Soup to emphasize that your ability to reason about these examples does not depend on what is true or false in the actual world.
If you know the meaning of the word no, and also know that the capital of a country is a city in that country, then you should be able to conclude that the two sentences in 6 are inconsistent, regardless of where Freedonia is or what the population of its capital is. That is, there's no possible situation in which both sentences could be true.
Similarly, if you know that the relation expressed by to the north of is asymmetric, then you should be able to conclude that the two sentences in 7 are inconsistent.
Broadly speaking, logic-based approaches to natural language semantics focus on those aspects of natural language which guide our judgments of consistency and inconsistency. The syntax of a logical language is designed to make these features formally explicit.
As a result, determining properties like consistency can often be reduced to symbolic manipulation, that is, to a task that can be carried out by a computer.
In order to pursue this approach, we first want to develop a technique for representing a possible situation. We do this in terms of something that logicians call a model. A model for a set W of sentences is a formal representation of a situation in which all the sentences in W are true.
The usual way of representing models involves set theory. The domain D of discourse all the entities we currently care about is a set of individuals, while relations are treated as sets built up from D.
Let's look at a concrete example. Our domain D will consist of three children, Stefan, Klaus and Evi, represented respectively as s, k and e. The expression boy denotes the set consisting of Stefan and Klaus, the expression girl denotes the set consisting of Evi, and the expression is running denotes the set consisting of Stefan and Evi.
Diagram of a model containing a domain D and subsets of D corresponding to the predicates boy, girl and is running. Later in this chapter we will use models to help evaluate the truth or falsity of English sentences, and in this way to illustrate some methods for representing meaning.
However, before going into more detail, let's put the discussion into a broader perspective, and link back to a topic that we briefly raised in 5.
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