Multi-Dimensional Modal Logic

Abstract

SCOPE OF THE SERIESLogic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing so demonstrates the underlying unity and applicability of logic.

Axioms, Algebras and Topology

“…Another promising avenue for extending the use of modal encodings is by the use of multi-dimensional modal logics [40,73,95], which are multi-modal logics, with different modalities ranging over orthogonal dimensions of their model structures. These have been used to capture both multiple spatial dimensions and the combination of space with time.…”

The grammar of quantification and the fine structure of interpretation contexts

“…A clear parallel between FOL semantics and the Kripke semantics for modal logic will emerge (see Ben-Shalom 1996, van Benthem 1997and Marx & Venema 1997: just as a formula in modal logic denotes a proposition / a sets of worlds, namely those worlds relative to which the formula is true, a formula in FOL denotes a set of assignments / a set of contexts, namely those contexts relative to which the formula is true. Moreover, existential quantification is like the possibility operator ♦ and universal quantification is like the necessity operator Ð; both of them, the accessibility relation is the binary relation over variable assignments induced by pointwise assignment manipulation, i.e., gÖυ×h.…”

Guards, Bounds, and Generalized Semantics

“…The resulting logic 'CRS' over general assignment models has been much studied (Marx & Venema 1997 Németi 1996). Instead, we turn to the connection between GAM-semantics for FOL and standard semantics for GF.…”