Merging Beliefs and Counterfactuals

Abstract

We present a unified framework for modeling

agents’ epistemic states and counterfactual conditionals.

The novelty of our approach lies at the

semantic level. We introduce a computationally

grounded semantics in which an agent’s doxastic

accessibility relation, needed to model the standard

notion of deductively closed belief, is derived from the agent’s belief base,

and in which the notion of comparative similarity between states,

needed to interpret counterfactual conditionals, is

computed from both the atomic formulas describing

the agents’ belief bases and those describing

the environment. We use this semantics to interpret a language

of beliefs and counterfactuals. We

demonstrate the expressiveness of our language and

the flexibility of the semantics by formalizing a

wide range of notions: counterfactual dependence,

counterfactual notions of reason and knowledge,

conditional belief. Furthermore, we show that our

semantics illuminates the subtle interplay between

belief change and counterfactuals. On the computational side,

we provide a succinct formulation of

model checking for our language and establish a

PSPACE complexity result.