Title: Strength Factors: An Uncertainty System for a Quantified Modal Logic,
Abstract: We present a new system S for handling uncertainty in a quantified modal
logic (first-order modal logic). The system is based on both probability theory
and proof theory. The system is derived from Chisholm's epistemology. We
concretize Chisholm's system by grounding his undefined and primitive (i.e.
foundational) concept of reasonablenes in probability and proof theory. S can
be useful in systems that have to interact with humans and provide
justifications for their uncertainty. As a demonstration of the system, we
apply the system to provide a solution to the lottery paradox. Another
advantage of the system is that it can be used to provide uncertainty values
for counterfactual statements. Counterfactuals are statements that an agent
knows for sure are false. Among other cases, counterfactuals are useful when
systems have to explain their actions to users. Uncertainties for
counterfactuals fall out naturally from our system.
Efficient reasoning in just simple first-order logic is a hard problem.
Resolution-based first-order reasoning systems have made significant progress
over the last several decades in building systems that have solved non-trivial
tasks (even unsolved conjectures in mathematics). We present a sketch of a
novel algorithm for reasoning that extends first-order resolution.
Finally, while there have been many systems of uncertainty for propositional
logics, first-order logics and propositional modal logics, there has been very
little work in building systems of uncertainty for first-order modal logics.
The work described below is in progress; and once finished will address this
lack.