A Two - Sorted Interpretation for Annotated LogicFl

Annotated Logic was introduced in Sub87] as a logic programming language to implement reasoning with uncertainty for knowledge-based systems. Later, it was shown to be adequate to formalise systems in which inconsistencies can be present, without trivialising its reasoning (technically coined \paraconsistent sys-tems" Cos63]). This Logic was generalised in BS88], but its foundational aspects were only developed years later CSV91, CAS91], when annotated propositional and rst-order calculi were presented. They are non-classical logics obtained from a positive logic with implication to which is added a weak negation operator. Recently, Annotated Logic has been advocated to be better suited to reason about uncertainty than with uncertainty CdS96]. It has also been proposed as a useful language to reason about arguments, rather than to reason with (logical) arguments about objective facts CCdS97].. In the present article we restate First-order Annotated Logic as a simple two-sorted classical rst-order language. Our goal is to expose some relations between this Logic and correspondence (i.e. relational) theories of truth Vis97], thus suggesting the application of this Logic as a exible tool to build relational theories of uncertainty.