Communication across Viewpoints
Dipartimento di Informatica, Universit?a di Pisa,
Corso Italia 40, I-56125 Pisa, Italy
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The situation which occurred in a dream provides the framework for discussing properties of the theory of viewpoints and in particular the issue of different denotations from different perspectives. We introduce the principle of referent sharing" in communications and argue that common knowledge resulting from communication should only use constants whose referent is manifest" to the parties involved.
Keywords: viewpoints, contexts, metalevel theories, reflective theories, natural deduction.
When several agents interact, their understanding of each other behaviour depends on some common knowledge they all share as well as on assumptions about each other private knowledge. The question arises then of how such common knowledge comes about. Communication between agents seems to involve two aspects: ensuring that they all understand the subjects of their sentences and becoming all aware that the information has been transferred.
The first aspect requires that the referents" in communications be shared. The second entails that communication not only involves transfer of knowledge from one agent to another but also extends their common knowledge. These two facts together imply that common knowledge resulting from communication should only use constants whose referent is manifest" to the parties involved.
We explore these issues in the framework of the theory of viewpoints [2, 4, 5]. This theory was conceived as a general and unified formalism for expressing several varieties of relativised truth: beliefs contexts, situations, truth, partitioning a knowledge base in microtheories and so on. Each of these notions can be represented through viewpoints whose specific properties are captured by axioms, added to the basic theory in order to characterise those viewpoints .
The theory of viewpoints is a reflective first order logic which amalgamates object and metalanguage by using names for each term and statement of the language and which contains an axiomatisation of provability in the style of natural deduction. Reflection rules provide the link between object and metalanguage and lead to a non conservative but consistent extension of first order logic; these rules