| |
Logic and Computation Group
Group Director
Dr. Vladimir Rybakov
Research Interests, Aims
The aim of this group is to investigate mathematical models for human reasoning
and their application to Computer Science and Artificial Intelligence. Basic
instruments for this research come from Mathematical Logic. A corner stone in
the basis of computing and Artificial Intelligence is the notion of logical
consequence. Being given information one has to derive consequences and facts
following from this information. The intelligence of reasoning (as a part of AI)
again requires the understanding of what are consistent consequences of
observable facts. Within Computer Science these aspects are involved in the
analysis of correct logical instructions or carrying out computations,
verification of programs and many other areas. In particular, Expert Systems
require mathematical analysis of consistent clauses from given information.
During computation the environment is changing simultaneously (in terms of
resources, available new information etc.). Therefore we need to develop
technique producing correct knowledge taking into account current of time and
changing conditions, and consequently we use temporal and modal logic. Some
major progress has been made in these fields, and, in particular, big attention
has been paid to developing techniques to handle multi-agent environments.
The main our aim is to develop theory of implicit logical clauses (i.e.
admissible inference rules) and to apply novel approaches from theory of
inference rules for non-standard logics, semantic tools for modal and temporal
logic to
- Investigation of temporal phenomena concerning derivation of information
from given facts (in particular, to develop a technique for recognizing implicit
clauses for various temporal logics.
- Investigation of knowledge representation within multi-agent based framework
(in particular, to construct effective algorithms verifying correctness of clauses
for logics of knowledge and agents believes, common knowledge logics)
- Study of logical systems modeling perception of agents and availability of
information for agents (in particular, to find Mathematical models - Kripke
models - describing perception and availability of information, to find basis for
correct implicit clauses within these logics).
Methods, Technique
We intend to analyze implicit clauses in the language of temporal, modal,
multi-modal logics, logics of reasoning about knowledge and beliefs for
multi-agent environments and common knowledge logics. Using of temporal logic
allows to analyze the history of agents knowledge and to anticipate the effect
of this knowledge in future. In its own right, modal and multi-modal logics
embrace fragments of temporal logics responsible only for future (for instance
next time logics), and they now are in grate demand because they are more
efficient method of obtaining positive results by reason of restricted language.
The technical instruments will include reduced normal forms of clauses, sharp
representing Kripke models, the theory of saturating possibilities, elements of
tableau and classical proof theory, elements from the theory of algebraic logics
and model theory for first-order logic.
Research Opportunities
If you are interested in postgraduate research at MPhil or PhD level then please
contact Prof. Dr V. Rybakov
|
|
