epistemic logic the logical investigation of epistemic concepts and statements. Epistemic concepts include the concepts of knowledge, reasonable belief, justification, evidence, certainty, and related notions. Epistemic logic is usually taken to include the logic of belief or doxastic logic. Much of the recent work on epistemic logic is based on the view that it is a branch of modal logic. In the early 1950s von Wright observed that the epistemic notions verified (known to be true), undecided, and falsified are related to each other in the same way as the alethic modalities necessary, contingent, and impossible, and behave logically in analogous ways. This analogy is not surprising in view of the fact that the meaning of modal concepts is often explained epistemically. For example, in the 1890s Peirce defined informational possibility as that ‘which in a given (state of) information is not perfectly known not to be true,’ and called informationally necessary ‘that which is perfectly known to be true.’ The modal logic of epistemic and doxastic concepts was studied systematically by Hintikka in his pioneering Knowledge and Belief (1962), which applied to the concepts of knowledge and belief the semantical method (the method of modal sets) that he had used earlier for the investigation of modal logic. In this approach, the truth of the proposition that a knows that p (briefly Kap) in a possible world (or situation) u is taken to mean that p holds in all epistemic alternatives of u; these are understood as worlds compatible with what a knows at u. If the relation of epistemic alternativeness is reflexive, the principle ‘KapPp’ (only what is the case can be known) is valid, and the assumption that the alternativeness relation is transitive validates the so-called KK-thesis, ‘Kap P KaKap’ (if a knows that p, a knows that a knows that p); these two assumptions together make the logic of knowledge similar to an S4-type modal logic. If the knowledge operator Ka and the corresponding epistemic possibility operator Pa are added to quantification theory with identity, it becomes possible to study the interplay between quantifiers and epistemic operators and the behavior of individual terms in epistemic contexts, and analyze such locutions as ‘a knows who (what) b (some F) is’. The problems of epistemic logic in this area are part of the general problem of giving a coherent semantical account of propositional attitudes.
If a proposition p is true in all epistemic alternatives of a given world, so are all logical consequences of p; thus the possible-worlds semantics of epistemic concepts outlined above leads to the result that a person knows all logical consequences of what he knows. This is a paradoxical conclusion; it is called the problem of logical omniscience. The solution of this problem requires a distinction between different levels of knowledge – for example, between tacit and explicit knowledge. A more realistic model of knowledge can be obtained by supplementing the basic possible-worlds account by an analysis of the processes by which the implicit knowledge can be activated and made explicit.
Modal epistemic logics have found fruitful applications in the recent work on knowledge representation and in the logic and semantics of questions and answers in which questions are interpreted as requests for knowledge or ‘epistemic imperatives.’
See also EPISTEMOLOGY , KK-THESIS, MODAL LOGI. R.Hi.