Sentences express propositions. If a sentence denotes a fact in reality, it is true; if not, it is false. Logicians and formal semanticists study under what circumstances a sentence is true. Those circumstances are called truth conditions. For example, for the sentence The King of Anpus is a dwarf to be true, there are a number of conditions: 1) Anpus is a kingdom (This is a made-up proper name); 2) there is a king in this country named Anpus; 3) the person on the throne is very small in size. As there is no country in the world today named Anpus, the sentence cannot be true. The example shows that sentences may be true under certain conditions. But there are sentences which are necessarily true. Compare:

　　(11)My uncle is male.
　　(12)My uncle is retired.

(11) is necessarily true. (12) may be true or false. The judgment of the truth of (2) cannot be made simply by understanding the meaning. Thus we can see two kinds of truth in (11) and (12) respectively. To use logical terms, (11) is analytically true, (12) is synthetically true.

　 Sentences may be related in sense. Here we will illustrate sense relations within and between sentences:

　·X is tautology:
　　(13)The bachelor is unmarried.
　　(The sentence is necessarily true. Yet the rheme does not provide any new information.)
　·X is contradiction:
　　(14)The bachelor is married.
　　(The sentence is necessarily false; the theme and the rheme are incompatible.)
　·X is inconsistent with Y:
　　(15) John is single.
　　(16) John is married.
　　(If John refers to the same person, the two sentences cannot be both true. One is true; the 　　other must be false.)
　·X is synonymous with Y:
　　(17) John broke the glass.
　　(18) The glass was broken by John.
　　(One is true, the other is also true. One is a paraphrase of the other.)
　·X entails Y:
　　(19) The meeting was chaired by a spinster.
　　(20) The meeting was chaired by a woman.
　　(If (19) is true, (20) is automatically true.)
　·X presupposes Y:
　　(21) Sam has returned the book.
　　(22) Sam borrowed a book.
　　((21) is true on the condition that (22) is true. Or: (22) is part of the assumed background against which (21) is said).

These semantic relations are found within or between meaningful sentences. There are sentences which sound grammatical but meaningless, such as:

　　(23)? Colorless green ideas sleep furiously.
　　(24)? The pregnant bachelor killed some phonemes.

(23) and (24) are said to be semantically anomalous.