Publication Details
Title: A Formalization of Viewpoints
Author: G. Attardi and M. Simi
Group: ICSI Technical Reports
Date: October 1993
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1993/tr-93-062.pdf
Overview:
We present a formalisation for the notion of "viewpoint," a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends first order predicate calculus through an axiomatization of provability and with the addition of proper reflection rules. The extension is not conservative, but consistency is granted. Viewpoints are defined as set of reified meta-level sentences. A proof theory for viewponts is developed which enables to carry out proofs of sentences involving several viewpoints. A semantic account of viewpoints is provided, dealing with issues of self referential theories and paradoxes, and exploiting the notion of "contextual entailment." Notions such as beliefs, knowledge, truth and situations can be uniformly modeled as provability in specialised viewpoints, obtained by imposing suitable constraints on viewpoints. Keywords: meta-level, logics for truth, belief and knowledge, situations, contexts
Bibliographic Information:
ICSI Technical Report TR-93-062
Bibliographic Reference:
G. Attardi and M. Simi. A Formalization of Viewpoints. ICSI Technical Report TR-93-062, October 1993
Author: G. Attardi and M. Simi
Group: ICSI Technical Reports
Date: October 1993
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1993/tr-93-062.pdf
Overview:
We present a formalisation for the notion of "viewpoint," a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends first order predicate calculus through an axiomatization of provability and with the addition of proper reflection rules. The extension is not conservative, but consistency is granted. Viewpoints are defined as set of reified meta-level sentences. A proof theory for viewponts is developed which enables to carry out proofs of sentences involving several viewpoints. A semantic account of viewpoints is provided, dealing with issues of self referential theories and paradoxes, and exploiting the notion of "contextual entailment." Notions such as beliefs, knowledge, truth and situations can be uniformly modeled as provability in specialised viewpoints, obtained by imposing suitable constraints on viewpoints. Keywords: meta-level, logics for truth, belief and knowledge, situations, contexts
Bibliographic Information:
ICSI Technical Report TR-93-062
Bibliographic Reference:
G. Attardi and M. Simi. A Formalization of Viewpoints. ICSI Technical Report TR-93-062, October 1993