### CIS Colloquium, Oct 08, 2015, 11:00AM - 12:00PM, SERC 306

### A Probabilistic First Order Logic

### Zoran Markovic , Mathematical Institute, Serbian Academy of Sciences and Arts

**Abstract**:

First order logic is extended with Keisler-style quantifiers, binding several variables in a
pair of formulas, expressing a statement of conditional probability. The values of
probability are non-standard (i.e., infinitesimals are allowed) so that approximate
probabilities may be represented and defaults can be modeled. Examples will be
presented showing the expressive power of this new logic which enables us to have, in
the same context (e.g., in the same data-base), statements of fact (true or false),
statements of probability, statements of approximate probability and defaults. It is also
possible to introduce new types of defaults – binary, and in general, n-ary defaults. Two
decidable fragments of the logic are defined, making the logic applicable in practice. The
logic is strongly complete, but the presentation will be oriented mainly toward examples
and possible applications.

**Bio**:

He received his Ph. D. from the University of Pennsylvania, Philadelphia in 1979. He was
the Director of the Mathematical Institute, Serbian Academy of Sciences and Arts
between 1985 and 2014. His research interests include intuitionistic, probabilistic and
non-monotonic logics, and their applications in Artificial Intelligence. He has been a
visiting scholar at the University of California, Berkeley, the University of California,
Davis, and the University of Amsterdam (Institute for Logic, Informatics and Linguistics).