Explicit/Implicit Belief and Derivational Systems

The problem of hyperintensional contexts, and the problem of logical omniscience, shows the severe limitation of possible-worlds semantics which is employed also in standard epistemic logic. As a solution, we deploy here hyperintensional semantics according to which the meaning of an expression is an abstract structured algorithm, namely Tichy's construction. Constructions determine the denotata of expressions. Propositional attitudes are modelled as attitudes towards constructions of truth values. Such a model of belief is, of course, inferentially restrictive. We therefore also propose a model of implicit knowledge, which is the collection of a possible agent's explicit beliefs which are related through a derivation system mastered by the agent. A derivation system consists of beliefs and derivation rules by means of which the agent may derive beliefs different from the beliefs she is actually related to. Conditions imposed on the set of base beliefs and the set of rules capture the limitations of the agent's deriving capabilities.