1.3.1 Being Systematic

Is there a systematic way of translating such simple sentences as ``John loves Mary'' and ``A woman walks'' into first-order logic?

The key to answering this question is to be more precise about what we mean by ``systematic''. When examining the sentence ``John loves Mary'', we see that its semantic content is (at least partially) captured by the first-order formula . Now this formula consists of the symbols , and . Thus, the most basic observation we can make about systematicity is the following: the proper name ``John'' contributes the constant symbol to the representation, the transitive verb ``loves'' contributes the relation symbol , and the proper name ``Mary'' contributes the constant symbol .

More generally, it's the words of which a sentence consists that contribute the relation symbols and constants in its semantic representation. But (important as it may be) this observation doesn't tell us everything we need to know about systematicity. It only tells us where the building blocks of our meaning representations will come from - namely from words in the lexicon.

But it doesn't tell us how to combine these building blocks. For example we have to form the first-order formula from the symbols , and . But from the same symbols we can also form . So why do we choose to put in the second argument slot of rather than in the first one? Is there a principle behind this decision? For this task, we haven't been specific yet about what we mean by working in a systematic fashion.