A FORMALIZATION OF VIEWPOINTS

Article type: Research Article

Authors: Attardi, Guiseppe | Simi, Maria

Affiliations: Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 1-56125 Pisa, Italy, [email protected], [email protected]

Abstract: 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 with its own metalanguage, an axiomatization of provability and 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 statements 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, absolute truth or truth relative to a situation can be uniformly modeled as provability in specialised viewpoints, obtained by imposing suitable constraints on viewpoints.

DOI: 10.3233/FI-1995-232341

Journal: Fundamenta Informaticae, vol. 23, no. 2-4, pp. 149-173, 1995