Modal Characterization of Visibility and Focus
نویسندگان
چکیده
Granular computing, based on rough set theory [1, 2], provides the basis for a new computing paradigm [3, 4]. Applying granular computing to logical reasoning processes, we have proposed granular reasoning for connecting possible world semantics and granular computing [5], and developed a granular reasoning framework called a zooming reasoning system [6–8]. The key concept of zooming reasoning system is focus, which represents atomic sentences that appear in each step of reasoning, where it is enough to consider truth values of atomic sentences used in the current step, letting us ignore truth values of other atomic sentences not used by constructing equivalent classes of possible worlds based on truth values of the atomic sentences appearing in the current reasoning step. Focus thus provides a three-valued truth valuation that assigns truth values true or false to atomic sentences that appear in focus and assigns a truth value unknown to other atomic sentences. In the zooming reasoning system, controlling the size of equivalent classes of possible worlds corresponds to reasoning. In redefining the concept of focus, we have introduced the granularity concept of visibility [9]. In granular reasoning, visibility and focus are analogies of terms in vision, representing the following concepts:
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