Algebraic Net Class Rewriting Systems, Syntax and Semantics for Knowledge Representation and Automated Problem Solving

TL;DR

This paper develops an algebraic framework for automated problem solving using generalized net rewriting systems, enabling the transformation and classification of knowledge representations for efficient solution derivation.

Contribution

It introduces a novel algebraic approach to knowledge representation and problem solving through net rewriting systems and congruent class constructions.

Findings

Established a universal algebraic framework for problem solving.

Derived solution algorithms parallel to candidate generation.

Created net automata-based acceptance criteria for solutions.

Abstract

The intention of the present study is to establish general framework for automated problem solving by approaching the task universal algebraically introducing knowledge as realizations of generalized free algebra based nets, graphs with gluing forms connecting in- and out-edges to nodes. Nets are caused to undergo transformations in conceptual level by type wise differentiated intervening net rewriting systems dispersing problems to abstract parts, matching being determined by substitution relations. Achieved sets of conceptual nets constitute congruent classes. New results are obtained within construction of problem solving systems where solution algorithms are derived parallel with other candidates applied to the same net classes. By applying parallel transducer paths consisting of net rewriting systems to net classes congruent quotient algebras are established and the manifested class rewriting comprises all solution candidates whenever produced nets are in anticipated languages liable to acceptance of net automata.