CADE-15 Workshop on
Many practical applications of deduction systems in mathematics, computer science, and artificial intelligence rely on the correct and efficient treatment of partial functions. For this purpose different approaches -- from workarounds for concrete situations to proper general treatments -- have been developed.
There are essentially three approaches to treating partiality, which further subdivide into a multitude of specialized logical systems. In the first category, undefined expressions are syntactically excluded. In the second, they are disregarded or bypassed. In the third, partiality is taken serious and this is reflected in the semantics and the calculus.
In order to make the distinction clear let us look at the treatment of division by zero. In the first approach terms like 1/0 are treated as syntactically ill-formed, for instance, by using a sorted logic. In the second approach a value is assigned to 1/0, either a fixed value (e.g. 0) or an undetermined one. In both cases it is necessary to tolerate undesired theorems. In the third approach, terms like 1/0 are not defined and semantically either uninterpreted or interpreted by some error element. In the same manner, atomic formulae, containing such an undefined term, like 1/0=0 are not interpreted by a truth value (true or false) at all or are interpreted by a third truth value (undefined). In a two-valued variant atomic formulae containing an undefined term are evaluated to false.
All approaches have their own advantages and disadvantages and are adequate for certain applications. The workshop would be devoted to discussing these advantages and disadvantages and relating the different approaches.
At CADE-13 in New Brunswick we organized a highly successful workshop on this topic. We would like to continue the scientific exchange in the new workshop. In addition to the last call, we like to explicitly call for contributions on applications of partiality.
The workshop will solicit for papers on (non-exclusive list):
Potential participants can apply either by submitting a short statement that contains a description of their current interests or, if they wish to make a (short or long) presentation, an abstract of the work they want to present. The short statements and abstracts should be sent by e-mail to Manfred Kerber, University of Birmingham, UK, M.Kerber@cs.bham.ac.uk by 21 May 1998.
Please include your postal address, e-mail address, and phone number. Final versions of accepted contributions are due by 12 June. They will be made available by WWW and will appear in an informal proceedings produced by CADE.
Those invited to attend the workshop have to register for the workshop in conjunction with the CADE main conference. Further information about the CADE is available here.