Justification for a Probabilistic Account of Conditionals

In this dissertation I argue that a probabilistic account of conditionals similar to the one proposed by Robert Stalnaker in 1968 is the logical account of conditionals that most aptly models conditional use in natural language. I argue that a probabilistic account of conditionals is best able to account for the most systematic and widespread uses of conditionals in natural language as is evidenced by both its compatibility with the descriptively accurate psychological account, as well as its ability to take into account expert intuitions that diverge from the material conditional interpretation. I provide expert support for Stalnakers account by describing the ways that a probabilistic conditional can avoid the paradoxes of the material conditional. I argue that the predictive accuracy of the alternative mental models account provides support for the claim that Stalnakers logical account of conditionals is descriptively accurate. I conclude that both expert and naive reasoners uses of conditional statements are most accurately modelled by a probabilistic account of conditionals similar to that proposed by Stalnaker

Proof Search in Hájek's Basic Logic.

2We introduce a proof system for H´ ajek’s logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL, are sound and invertible with respect to any valuation of BL into a suitable algebra, called (ω)[0, 1]. Refining the notion of reduction tree that arises naturally from RHBL, we obtain a decision algorithm for BL provability whose running time upper bound is 2O(n), where n is the number of connectives of the input formula. Moreover, if a formula is unprovable, we exploit the constructiveness of a polynomial time algorithm for leaves validity for providing a procedure to build countermodels in (ω)[0, 1]. Finally, since the size of the reduction tree branches is O(n3), we can describe a polynomial time verification algorithm for BL unprovability.reservedmixedBova S.; Montagna F.Bova, S.; Montagna, Franc