Events rn the semantrcs of Englrsh. -Cambridge, Massachusetts: MIT
- Parsons, Terence
There has been much early work on variable-free semantics and I will not attempt to review that here, but only mention the important systematic recent work of Tarski and Givant . As is familiar to many people, Tarski and Givant show that a variable-free formalization of set theory can express a large part of standard mathematics, a lnuch larger part than almost anybody would expect to be the case. They also establish the limitations of the system where the expressive power breaks down, but I shall not expand on the details here. I use this as reference because o f its encouraging character. Concerning my own prior \vork on variable-free semantics, the work on loglcal inference ln English [lo] 1s the most relevant, but I shall not review I t here. We can expect to do a great deal with variable-free semantics, even in the context of mathematical objects as complicated as stochastic processes. For a full treatment of stochastic processes, we would also need a much more explicit lexical semantics than I have given in any previous work, or than has in general been given by anyone else dealing with variable-free semantics for ordinary English or somt other natural language. Fc~llowlng a hallowed tradition, I will omit the discussion of lcxlcal semantics. I just want to remark that i n recent detailed work on robotics and on physics word problems, we have found that I t is absolutely essential to enter into the lexical semantics In some detail.