Combining Propositional Logic with Maximum
Entropy Reasoning on Probability Models
Manfred Schramm
Stephan Schulz
We present a system for non-monotonic reasoning based on the
probability calculus. This calculus incorporates this type of
reasoning in two ways: Non-monotonic decisions (which can be treated
as decisions under incomplete knowledge as well) can be the result
of reasoning in a single probability model (via conditionalization)
or in a set of probability models (via additional principles of
rational decisions). But probability theory is too fine-grained to
model common sense reasoning in general (think about "paradoxes" due
to the unexpected existence of certain P-Models (\cite{Bl72,NH90})).
The remaining degrees of freedom have to be filled (of course
without introducing subjective biases). We therefore use additional
(context-sensitive) constraints (resp. principles), which are able
to support rational decisions based on incomplete know\-ledge. These
principles have to be global (context-dependent on all assumptions)
to avoid loosing the sensitivity of the language to the assumptions.
The central principle of rational decisions used by our system is
the method of Maximum Entropy (MaxEnt), which is a well founded
extension of probability theory with global properties
(\cite{Ja95,Ja78,GMP90,PV90}).