Bounded rationality and logic for epistemic modals

Abstract

Kratzer (1991) provides comparative epistemic modals such as ‘at least as likely as’ with their models in terms of a qualitative ordering. Yalcin (2010) shows that Kratzer’s model does not validate some intuitively valid inference schemata and validates some intuitively invalid ones. He adopts a model based directly on a probability measure for comparative epistemic modals. His model does not cause this problem. However, as Kratzer (2012) says, Yalcin’s model seems to be unnatural as a model for comparative epistemic modals. Holliday and Icard (2013) prove that not only a probability measure model but also a qualitatively additive measure model and a revised version of Kratzer’s model do not cause Yalcin’s problem. Suzuki (2013) proposes a logic the model of which reflects Kratzer’s intuition above, does not cause Yalcin’s problem, and has no limitation of the size of the domain. In the models of Holliday and Icard (2013) and Suzuki (2013), the transitivity of probabilistic indifference is valid. The transitivity of probabilistic indifference can lead to a sorites paradox. The nontransitivity of probabilistic indifference can be regarded as a manifestation of bounded rationality. The aim of this paper is to propose a new version of complete logic—Boundedly-Rational Logic for Epistemic Modals (BLE)—the model of the language of which has the following three merits: (1) The model reflects Kratzer’s intuition above in the sense that the model should not be based directly on probability measures, but based on qualitative probability orderings. (2) The model does not cause Yalcin’s problem. (3) The model is boundedly-rational in the sense that the transitivity of probabilistic indifference is not valid. So it does not invite the sorites paradox.