Case-by-Case Problem Solving Pei Wang Temple University Philadelphia, USA

Algorithmic Problem Solving Use a computer to solve a problem:  Problem is a class, solution is an algorithm e.g., “sorting” to “quicksort”  Problem is an instance, solution is a result e.g., “sort [3, 2, 4, 1]” to “[1, 2, 3, 4]” The former is done by human, the latter is done by computer following the algorithm

No algorithm for it? What if the computer has no algorithm for a problem instance?  Use a general-purpose algorithm e.g., state-space search  Find an algorithm first e.g., machine learning

Solving it without algorithm?! How about to directly solve the problem instance without following an algorithm? “Nonsense! How can a computer run without algorithms?” “But this process can still be carried out by algorithms not defined for this problem. An algorithm for problem P is not an algorithm for problem Q, right?”

Case-by-case problem solving  NARS represents a problem (instance) as an inference task, to be processed by a set of general-purpose inference rules  Rule selection is knowledge-driven, rather than algorithm-guided  Knowledge selection is context-sensitive  Inference process is resource-restricted

Scopes of input-output  Each operation in NARS is controlled by certain algorithm, with fixed input-output mapping (see code)code  The lifelong experience of the system fully determines its lifelong behaviors (see examples)examples  However, there is no function that maps “problem” to “solution”

Properties of CPS CPS and APS are suitable for different (knowledge/resources) situations In CPS, the following notions are different:  Problem  Solution  Solvable problems  Resource cost of a problem  Scaling up …