TY: CHAP
T1 - Rigid first-order hybrid logic
A1 - Blackburn, Patrick
A1 - Martins, Manuel
A1 - Manzano, Marķa
A1 - Huertas, Antonia
N2 - Hybrid logic is usually viewed as a variant of modal logic
in which it is possible to refer to worlds. But when one moves beyond
propositional hybrid logic to first- or higher-order hybrid logic, it becomes useful to view it as a systematic modal language of rigidification. The key
point is this: @ can be used to rigidify not merely formulas, but other
types of symbol as well. This idea was first explored in first-order hybrid
logic (without function symbols) where @ was used to rigidify the firstorder constants. It has since been used in hybrid type-theory: here one
only has function symbols, but they are of every finite type, and @ can
rigidify any of them. This paper fills the remaining gap: it introduces a
first-order hybrid language which handles function symbols, and allows
predicate symbols to be rigidified. The basic idea is straightforward, but
there is a slight complication: transferring information about rigidity
between the level of terms and formulas. We develop a syntax to deal
with this, provide an axiomatization, and prove a strong completeness
result for a varying domain (actualist) semantics.
UR - https://ria.ua.pt/handle/10773/26443
Y1 - 2019
PB - Springer Verlag