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					                                      SEMANTIC FIELD

                                          Germano Resconi

                          Università Cattolica Dipartimento di Matematica
                                Via Tireste 17 ,25100 Brescia Italy

Recently, Resconi, Klir, Harmanec, and St.Clair have developed in a series of their paper2,3,4 new
hierarchical uncertainty metatheory based upon modal logic. This new approach enables us to
collect various different uncertainty theories including fuzzy set theory, Dempster-Shafer theory of
evidence, and possibility theory in one metatheory. The most difficult point in the metatheory is to
define the possible worlds and the accessibility relation between possible worlds.
     In order to overcome the difficulties, we propose in this paper the concept of degree of
significance that is the support for the semantic field in the space of the possible worlds. By the
semantic field and degree of significance, we define accessibility relations and we give a set
representation for the metatheory based upon modal logic.
      The semantic field is the mathematical support for introspective information for human being.
With Kripke models, inferential rules are possible among the worlds. Because at any sentence in
logic we can associate a part of the semantic field, any conclusion of a chain of inferential
deductions can be shown by semantic field. One use the tool of the field theory and the other the
tool of inferential process to describe uncertainty in information and also to discover logic structure
inside the data.
    The type of Kripke model for modal logic to use is connected with the structure of the semantic
field. The logic is not fixed but is flexible and dynamic by depending on the field in a space time
reference. A completely sure event is described by only one world. When uncertainty arises, the
world will be split in many possible worlds. In this way we can generate the space of worlds. With
this space we can represent the probability and the fuzzy sets theories of the uncertainty. To describe
also belief and plausibility measures in Dempster-Shafer theory we use the variation of the semantic
field as accessibility relation. One world is accessible to another world when its semantic field is
higher to the other. Semantic field is the information that establishes a level of significance to any
world. Semantic field is the fundamental element by which we can integrate many different type of
uncertainty measures .Any semantic field is a virtual field that can be implemented by a physical
field as electromagnetic field, chemical concentration field or other field. This field becomes the
connector of many different unity of calculus located in any world. We suggest, for future
application, modal logic and semantic field can be useful as tool to create a semantic
  T.Murai, M.Nakata, and M.Shimbo, Ambiguity, Inconsistency, and possible-worlds: a new logical
approach. Proceeding of the Ninth Conference on Intelligence Technologies in Human-Related
Sciences, Leòn, Spain, 1996, pp.177-184
   G.Resconi, G.J.Klir, and U.St.Clair, Hierarchical Uncertainty Metatheory Based upon Modal
Logic. Int. J. of General Systems, Vol.21 (1992), pp.23-50.
  G.Resconi, G.J.Klir, U.St.Clair, and D.Harmanec, On the Integration of Uncertainty Theories.
Int.J.of Uncertainty, Fuzziness, and Knowledge-Based Systems, Vol.1 (1993), pp.1-18.
  G.Resconi, G.J.Klir, D.Harmanec, and U.St.Clair, Interpretations of Various Uncertainty Theories
Using Models of Modal Logics: A Summary. Fuzzy Sets and Systems, Vol.80 (1996), pp.7-14.
  G.Resconi , T.Murai , Field Theory and Modal Logic by Semantic Field to Make Uncertainty
Emerge from Information, will be appear on the Int.J.General System (1999)

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