propositional

9/1/12

Skills to be acquired in this tutorial:

Symbolizing compound propositions. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.

Why this is useful:

It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.

8/25/12

Not all propositions are atomic propositions. Consider the proposition asserted by 'It is not the case that in 2011 the United States had a female President'. This is a true proposition, yet it is not an atomic one. It is made up of the atomic proposition 'in 2011 the United States had a female President' (which is false) and negation (expressed by 'It is not the case that...'), and the resulting compound proposition, which is the negation of a false proposition, is true.

There are several types of compound proposition.

8/25/12

The symbolization of English statements or propositions can be done using instruments of varying degrees of logical sophistication. The presentation here is restricted to propositional and predicate logic. Researchers in linguistics, philosophical logic, advanced computer science, or artificial intelligence would likely use some more advanced form of logic. However, predicate logic, encompassing propositional logic, is not introductory and it is entirely adequate for many purposes. Being familiar with it is worthwhile intellectually (and it is non-trivial to learn).

8/25/12

In English there is usually more than one way to say the same thing. For example, the sentences 'Forests are widespread or grass is plentiful.' and 'Either forests are widespread or grass is plentiful.' assert the same compound proposition-- the new word 'either' at the beginning of the second sentence does not alter the underlying logical structure. Both these sentences should be symbolized to (F∨G).

One symbolic formula can represent the logical structure of a proposition asserted by several different English sentences (this is one reason why we symbolize).