Ockhamistic logics and true futures of counterfactual moments
Torben Braüner, Per Hasle, Peter Øhrstrøm · 2002
Various Ockhamistic logics are compared, with the aim of making clear the role of true futures of counterfactual moments, i.e. true futures of moments outside the true chronicle. First, we give an account of A.N. Prior's (1967) original Ockhamistic semantics, where the truth of a formula is relative to a moment and a chronicle. We prove that this is equivalent to a semantics put forward by Thomason and Gupta (1980), where truth is relative to a moment and a so-called chronicle function which assigns a chronicle to each moment. This is the case because true futures of counterfactual moments do not matter in Thomson and Gupta's semantics. Later, we discuss how two options considered by Belnap and Green (1994) might be formalised. They come about by associating either a chronicle or a chronicle function to be given once and for all. The first of the two options is unable to give an account of certain statements from natural language, and the second option invalidates an intuitively valid formula. We propose a new Ockhamistic semantics where the formula in question is valid, and furthermore, where true features of counterfactual moments are taken into account. Finally, we discuss possible applications within artificial intelligence.