Modal Foundations for Predicate Logic

The complexity of any logical modeling reflects both the intrinsic structure of a topic described and the weight of the formal tools. Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. In this paper, we investigate `lighter' versions of this general purpose tool, by modally `deconstructing' the usual semantics, and locating implicit choice points in its set up. The first part sets out the interest of this program and the modal techniques employed, while the second part provides technical elaborations demonstrating its viability. Keywords: quantifier, variable, dependency, modality, cylindric algebra 1 The modal core of predicate logic The well-known standard semantics for predicate logic has the following key clause: M; a j= 9xOE iff for some d 2 jMj : M; ff x d j= OE: Tarsk's main innovation here was the use of assignments, which are essential in decomposing quantified statements, which leave free variabl..