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Valuation function V/Bigelow/Pargetter: its definition is complex because it has to be recursive. It assigns an interpretation or a semantic value. (To each expression of the language).
Valuation: First, semantic values are assigned to the non-logical constants.
Rules are then created for semantic values from compound expressions.
Logical constants: their valuation is specified by recursive rules.
Domain: can also be restricted, e.g. if you want to exclude the Barcan formula.
For example, restriction: for each world w you can assume a separate individual domain DW. Which, for example, consists only of the possibilia of this possible world.
Definition partition/Bigelow/Pargetter: is a family of individual domains that do not overlap. I.e. no individual is in more than one possible world. That would correspond to Lewis's counterpart theory.
Counterfactual Conditional/Valuation/Valuation Function/Valuation Rules/Bigelow/Pargetter:
V9 If a = (ß would be γ) then V (a) is the set of all possible worlds w ε w so that there is a possible world u where ß is true and γ is true and every possible world v in which ß is true and γ is false, is less accessible from w than from u. (s) > similarity metrics.
Similarity/possible worlds/similarity metrics/counterfactual conditional/Bigelow/Pargetter: Rule V9 states that a counterfactual conditional (ß would be > would be γ) is true in a possible world if the next ß-worlds are all γ-worlds._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990