Evidentialist Logic
Matthew P. Wampler-Doty

Abstract:
The purpose of this thesis is to present a formal framework which
tries to present a novel modal logic for reasoning about
knowledge. Subsequently, we shall conform to the following structure:

§1 First, we shall elaborate the on our philosophical intuition
   behind our epistemic logic, and provide a sketch of how the system
   will ultimately be formulated.

§2 Next, we give formal details of the system we will
   develop. Single agent semantics for concrete models is developed
   and an elimination theorem is derived. The semantics are then
   extended to a multi-agent setting, and finally Kripke semantics as
   an abstraction on our previous concrete semantics.

§3 Here we present several axiom systems for the abstract and
   concrete semantics. We show via our investigated completeness
   results that Kripke semantics faithfully abstracts away from our
   concrete semantics. We also derive the small model property for all
   of the axiom systems we provide, and discuss their
   inter-relationships in terms of a lattice of conservative
   extensions.  Some complexity results are also provided.

§4 Finally. we shall look at applications of the framework
   developed. We show that imposing certain popular axioms leads to
   collapse results for concrete EviL models and Kripke seman-
   tics. We then provide three embeddings of intuitionistic logic into
   EviL, and discuss some of their connections to the philosophical
   literature.

§5 Finally, the framework developed shall be compared to other approaches.