Semantics in Banach spaces (Q802541)

The aim of this paper is to call attention of logicians and philosophers to the possibility of formulating semantics in terms of functional analysis concepts. A new approach to semantics is proposed, whose basic concept is that of an ordered Banach space. This formulation of semantics arises as a natural generalization of the Giles' approach to belief structures and, at the same time, of the so-called ''fuzzy extensions'' of Boolean as well as of non-Boolean semantics. Finally, it should be remarked that some independent motivation for applications of ordered Banach spaces in semantics can be found in the so-called ''operational approach'' to the foundations of quantum mechanics.