Problem Reduction as a general epistemic reasoning method

EasyChair Preprint 1208

Abstract

We introduce a reasoning method based on problem reduction and show its use in several disciplines.

We consider a problem (problem domain) P = (I, S, A) consisting of set of problem instances I, set of potential solutions S and acceptability relation A is a subset of I x S.

Problem reduction occurs e.g. when a real world problem is reduced to a model, or finding a solution is delegated to an agent with richer knowledge.

Assume we have two problem domains P1 = (I1, S1, A1) and P2 = (I2, S2, A2). Reduction of a problem P1 to a problem P2 consists of a pair of mappings (r, t): r (reduction) maps problem instances i1 in I1 of P1 to problem instances r(i1) in I2 of P2 and t (transfer) maps solutions s2 in S2 to solutions t(s2) in S1 in such a way, that an acceptable (in the sense of relation A2) solution s2 to instance r(i1) is transferred to an solution t(s2) which is A1-acceptable to original problem instance i1. Formally: for all i1 in I1 and s2 in S2

                      A2(r(i1), s2) implies A1(i1, t(s2)) holds true constructively.

Our approach generalizes analogical reasoning [A], in that we show that along of similarity it works also under some quite complementary situations

Following [He] we can read following question-answer: SPIEGEL: And what now takes the place of Philosophy? Heidegger: Cybernetics. We will show that problem reduction can be used to understanding cybernetics as modeling (reducing reality to a model).

Peter Senge’s [S] organizational analysis’ depth with the different type of possible actions (solutions) can be understood as problem reduction.

 [A] P. Bartha, Analogy and Analogical Reasoning, The Stanford Encyclopedia of Philosophy

 [He] M. Heidegger, Only a God Can Save Us, Der Spiegel. 1976-05-31

[S] P. Senge. The Fifth Discipline. Doubleday, New York 1990

Keyphrases: Heidegger interview, Reasoning method, System sciences, analogical reasoning, cybernetics, decision support, organizational envisioning and narration

@booklet{EasyChair:1208,
  author    = {Peter Vojtas and Michal Vojtas},
  title     = {Problem Reduction as a general epistemic reasoning method},
  howpublished = {EasyChair Preprint 1208},
  year      = {EasyChair, 2019}}