cuted actions. It has been applied to several challenge problems in the theory of commonsense knowledge. We study the relationship between this formalism and other work on nonmonotonic reasoning and knowl-.

This papers gives a survey of recent results about simulations of one class of modal logics by another class and of the transfer of properties of modal logics under extensions of the underlying modal language. We discuss: the transfer from normal polymodal logics to their fusions, the transfer from normal modal logics to their extensions by adding the universal modality, and the transfer from normal monomodal logics to minimal tense extensions. Likewise, we discuss simulations of normal polymodal logics by normal (...) monomodal logics, of nominals and the difference operator by normal operators, of monotonic monomodal logics by normal bimodal logics, of polyadic normal modal logics by polymodal normal modal logics, and of intuitionistic modal logics by normal bimodal logics. (shrink)

A practical system of reasoning must be both correct and efficient. An efficient system which contains a large body of information can not search for the proof of a conclusion from all information available. Efficiency requires that deduction of the conclusion be carried out in a modular way using only a relatively small and quickly identified subset of the total information. One might assume that data modularity is incompatible with correctness, where a system is correct for a logic L iff (...) it proves exactly what is valid in L. We point out that modularity and correctness are indeed incompatible if the logic in question is classical. On the other hand, the two desiderata are compatible for relevance logic. Furthermore, Horn clause resolution theorem proving is modular (this helps explain its relative efficiency) and the logic for which it is correct is relevance logic not classical logic. (shrink)

In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.