AbstractsPhilosophy & Theology

A Fitch-style derivation system for hybrid logic

by Jared Smith

Institution: University of Georgia
Department: Philosophy
Degree: MA
Year: 2014
Keywords: Hybrid Logic, Modal Logic, Fitch-style Natural Deduction
Record ID: 2024655
Full text PDF: http://purl.galileo.usg.edu/uga_etd/smith_jared_201405_ma


Standard modal logic is typically parsed as concerning possible worlds. However there is no way for normal modal logic to refer to those possible worlds directly, which hampers its expressiveness. Hybrid logic develops tools to talk about particular possible worlds and so avoids the curtailed expressive power modal logic possesses. There are several proof systems for hybrid logic. Here I develop one in Fitch-style. This type of proof system naturally fits the goals of hybrid logic because of its clarity and resemblance to our natural process of reasoning. I prove this newly developed system is equivalent to established systems for building proofs in hybrid logic. Finally I examine what traits we should look for in a proof system.