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An investigation of modal structures as an alternative semantic basis for epistemic logics
Author(s) -
Hamilton Sharon J.,
Delgrande James P.
Publication year - 1989
Publication title -
computational intelligence
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 52
eISSN - 1467-8640
pISSN - 0824-7935
DOI - 10.1111/j.1467-8640.1989.tb00318.x
Subject(s) - kripke semantics , modal , accessibility relation , kripke structure , normal modal logic , modal logic , computer science , possible world , basis (linear algebra) , extension (predicate logic) , mathematics , epistemology , algorithm , philosophy , model checking , geometry , polymer chemistry , chemistry , programming language
In the past, Kripke structures have been used to specify the semantic theory of various modal logics. More recently, modal structures have been developed as an alternative to Kripke structures for providing the semantics of such logics. While these approaches are equivalent in a certain sense, it has been argued that modal structures provide a more appropriate basis for representing the modal notions of knowledge and belief. Since these notions, rather than the traditional notions of necessity and possibility, are of particular interest to artificial intelligence, it is of interest to examine the applicability and versatility of these structures. This paper presents an investigation of modal structures by examining how they may be extended to account for generalizations of Kripke structures. To begin with, we present an alternative formulation of modal structures in terms of trees; this formulation emphasizes the relation between Kripke structures and modal structures, by showing how the latter may be obtained from the former by means of a three‐step transformation. Following this, we show how modal structures may be extended to represent generalizations of possible worlds, and to represent generalizations of accessibility between possible worlds. Lastly, we show how modal structures may be used in the case of a full first‐order system. In all cases, the extensions are shown to be equivalent to the corresponding extension of Kripke structures.