Backwards-Looking Operators in Tense Logic and in Natural Language

This paper contains two parts. In the first one, we shall argue that in the tense system of English there are particles which are best analysed as, what we call, backwards-looking operators. By means of these operators (whose formal counterparts are to a large extent new in the literature) we shall establish the following limiting thesis concerning an adequate semantics for English tenses: For all natural numbers n, the semantics should have a capacity to keep track of n points introduced earlier in an evaluation. In the second part of this paper, we shall present a formal language which contains operators of this new kind. We formulate explicit model theory for this formal language in Hintikka's game-theoretical semantics. This semantical approach is sufficiently rich to satisfy the condition laid down by the limiting thesis mentioned.