Can Domain Specific Knowledge Be Generalized?

CAN DOMAIN Sl'ECI,FIC KNOWLEDGE BE GENERALIZED?

Alan Bundy Department of Artificial Intelligence University of Edinburgh Scotland

The MECHO project (see [1]) consists of writ­ ing a computer program which can colve a wide var­ iety of simple mechanics problems stated inEnglish. This program is being used as a vehicle for study­ ing methods for guiding search in a semantically rich domain. Our methodology is to find general, justifiable, inference rules which can be combined to carry out the reasoning necessary to solve the mechanics problems. As is well known, when rules like these are run on a general inference machine the result is often a combinatorial explosion. Rules are combined in unexpected ways and the search for a solution is developed along unreason­ able paths. These failures are used to debug the rules by adding to them local, domain specific control information. Finally these techniquesare generalized and incorporated in the inference mechanism. we hope that this methodology will lead us to the design of a computational logic for natural reasoning.

In this paper one such transition from domain specific to general inference technique will be described. we will use this example to emphasize the importance of this generalization stage. With­ out it one might be led to superficial and false conclusions about the nature of natural reasoning.

Suppose we have available the following re­ lations: Vel(Object, v, time) - (v is the velocity of object during time); -

At(Object, place, moment) - (object is at place at moment); Final(period, moment) - (moment is the final moment of time interval perio~We may have discovered the following domain specific in­ formation enabling us to guide the search for problem solutions along successful lines.

• (i) If the program is desperate to satisfy Vel(Object, v, time), object and time being known, but all inferences have ground to a halt, then a new intermediate unknown v can be created and as­ serted to be the velocity-of object at time.
• (ii) If the program is asked to confirm that At(object, placel, moment), but it already knows that object is at some different place (place2) at moment, then the attempt to prove

At(object, placel, moment) can be abandoned, be­ cause objects can only be in one place at a time. (iii) If the final moment of period is found to be momentl, but later processing fails, it is no use backing up to recalculate Final(period, ?x), since the same answer is bound to be given.

At first glance it might seem as if these ex­ amples argued for the intervention of rich domain specific information at all control points and that a programming language which facilitated such intervention was required. But these conclusions are not justified from the examples (i)-(iii) above. In fact (i)-(iii) represent different facets of a general phenomenon. To see this notice that Vel, At and Final are all really functions: Vel is a function from objects and times to velocities; At is a function from objects and moments to places and Final is a function from periods to moments. What separates functions from other relations is that they are single valued, that is their value is guaranteed to exist and to be unique. ·(i) is an example of this existence property being used and (ii) and (iii) different uses of the unique­ ness property. The generalizations of (i), (ii) and (iii) are

(i) ' If the program is desperate to find a func­ tion value given its arguments, and all inferences have failed then a new entity can be created and asserted to be that value. (Note that we do not want th.e program to create a new entity whenever it is legal to do so as this contributes to the com­ binatorial explosion. The notion of being des­ perate for the answer can be generalized (see [2]). (ii) ' If the program is trying to confirm a func­ tion value, but it already has a contradictory value stored then the confirmation attempt is to be abandoned.

(iii) ' If the program has calculated a function value then it should not recalculate this on back up.

Note that (i) '-(iii)' improve on the predicate calculus representation of the existence andunique­ ness of function values, by giving procedural in­ formation about when this information is to be used. They also improve on the local domain specific em­ bodiment of (i)-(iii) by representing a large . amount of such information in concise form, e.g. the existence property can now be used on At and Final and the uniqueness property can be used on Vel. All that is necessary to share the benefits of the control information embodied in (i) '-(iii)'

is to specify which relations have function values.

For functions of one argument the_implement­ ation of (i) '-(iii)' can be assisted by maintain­ ing a single slot on the property l i st of the argu­ ment. However, something more complicated is

needed for functions of more than one argument.

Some relations may be functions in more than one way, e.g. if Timesys(period, initmom, finmom) means that initmom is the initial moment and finmom is the final moment of period then Timesys is __ a __ __

function in 3 ways:

• (a) from period to initmom
• (b) from period to finmom
• (c) from initmom and finmom to period