Propositional Logic - artificial intelligence:

This is a limited logic, which permit  us to write sentences about propositions - statements about the world - which can either be false or  true. The symbols in this logic are (i) connectives which are: and (∧), or (∨), not (¬),  and implies (->) (ii) capital letters such as Q,P and R which represent propositions such as: "It is raining" and "I am wet", (iii) brackets and (iv) T which stands for the proposition "true", and F which stands for the proposition "false". The syntax of this logic are the rules specifying where in a sentence the connectives may go, for example ∨ might go between two propositions, or between a bracketed conjunction of propositions and so on .

The semantics of this logic are rules about how to assign truth values to a sentence if we know whether the propositions mentioned in the sentence are true or not.  One rule is that the sentence P ∨ Q is true in the situation only when P and Q both are true. The rules also dictate how to use brackets.  As a very simple example, we may represent the knowledge in English that "I always get wet and annoyed when it rains" as:

I am wet -> It is raining ∧ I am annoyed

If we program our agent with the semantics of propositional logic, then if at some stage, we tell it that it is raining; it can infer that I will get wet and annoyed.