Foundations of conditional logic (Q796516)

The linguistic particle ''if'' can be viewed as a generalized quantifier, relating sets of antecedent occasions and consequent occasions for a conditional statement. In this light, the recent logico-linguistic work on generalized quantifiers becomes available as a tool for studying conditional expressions. This paper presents an analysis of some basic constraints on such conditional relations. Then, various definability results are proven - notably one showing that, without further patterning of the universe of occasions, only three conditionals qualify. Hence, richer approaches, infinitary, probabilistic and intensional, are also studied in the same spirit. Finally, some basic conditional logics, and eventually conditional inference in general, are examined as to their semantic effects in this framework.