T2.3: 6 of 6

Syntax, AKA Grammar

Our task here is to show how sentences are properly constructed. Let's start with SL without names, then add them at the end of the page. 























We will call the simplest sentences of our language the atomic sentences of SL. These building blocks include 'A','B','C','D'..., 'Z' (except we won't use the 'V' to avoid confusion with the wedge 'v').

The atomic sentences, as their name implies, are used as the basic building blocks for SL sentences. You use them to construct longer sentences, molecular sentences, like the following four sentences:

a. (A&B)
b. ~L 
c. (~L>C)
d. ((A&B)=(~L>C))

(Notice that we do not yet drop outside parentheses. But we will let you drop these.) The idea behind the definition of an SL sentence can be put as follows:

































An example of sentence construction














     Moving on...

























Here's all that sentence construction written down:


























We can now add two ammendments to the definition:

  1. For clarity, you may
    • drop outside parentheses and write, e.g., '~B&(~CvA)' instead of '(~B&(~CvA))' AND when it helps,
    • use brackets instead of parentheses like so: '~[~B&(~CvA)]'.

  2. You can use names: add 'Ac' etc. (upper case followed by lower case 'a'-'u') to the stock of atomic sentences.